There is some problem in databases upgrade scripts.
1 export db from zabbix 2.0.4
2 import to new schema, on postgres 9.3.2
3 Start zabbix_server
4 cat the logs:

[root@Zabbix ~]# cat /tmp/zabbix_server.log
13810:20140207:073912.959 Starting Zabbix Server. Zabbix 2.2.2rc2 (revision 42257).
13810:20140207:073912.959 ****** Enabled features ******
13810:20140207:073912.959 SNMP monitoring: YES
13810:20140207:073912.959 IPMI monitoring: NO
13810:20140207:073912.959 WEB monitoring: YES
13810:20140207:073912.959 VMware monitoring: YES
13810:20140207:073912.959 Jabber notifications: NO
13810:20140207:073912.959 Ez Texting notifications: YES
13810:20140207:073912.959 ODBC: NO
13810:20140207:073912.959 SSH2 support: YES
13810:20140207:073912.959 IPv6 support: NO
13810:20140207:073912.959 ******************************
13810:20140207:073912.959 NodeID: 1
13810:20140207:073912.959 ******************************
13810:20140207:073912.959 using configuration file: /etc/zabbix/zabbix_server.conf
13810:20140207:073912.959 In load_modules()
13810:20140207:073912.959 End of load_modules():SUCCEED
13810:20140207:073912.959 In init_database_cache()
13810:20140207:073912.959 In zbx_mem_required_size() size:0 chunks_num:4 descr:'history cache' param:'HistoryCacheSize'
13810:20140207:073912.959 End of zbx_mem_required_size() size:543
13810:20140207:073912.959 In zbx_mem_create() descr:'history cache' param:'HistoryCacheSize' size:268435415
13810:20140207:073912.959 zbx_shmget() removing existing shm_id:5177345
13810:20140207:073912.959 valid user addresses: [0x7f1afc7be170, 0x7f1b0c7bdfc8] total size: 268435032
13810:20140207:073912.959 End of zbx_mem_create()
13810:20140207:073912.959 In zbx_mem_required_size() size:0 chunks_num:1 descr:'history text cache' param:'HistoryTextCacheSize'
13810:20140207:073912.959 End of zbx_mem_required_size() size:435
13810:20140207:073912.959 In zbx_mem_create() descr:'history text cache' param:'HistoryTextCacheSize' size:67108864
13810:20140207:073912.959 zbx_shmget() removing existing shm_id:5210114
13810:20140207:073912.959 valid user addresses: [0x7f1af87be178, 0x7f1afc7bdff0] total size: 67108472
13810:20140207:073912.959 End of zbx_mem_create()
13810:20140207:073912.959 In init_trend_cache()
13810:20140207:073912.959 In zbx_mem_required_size() size:0 chunks_num:1 descr:'trend cache' param:'TrendCacheSize'
13810:20140207:073912.959 End of zbx_mem_required_size() size:422
13810:20140207:073912.959 In zbx_mem_create() descr:'trend cache' param:'TrendCacheSize' size:16777216
13810:20140207:073912.959 zbx_shmget() removing existing shm_id:5242883
13810:20140207:073912.959 valid user addresses: [0x7f1af77be170, 0x7f1af87bdff0] total size: 16776832
13810:20140207:073912.959 End of zbx_mem_create()
13810:20140207:073912.959 End of init_trend_cache()
13810:20140207:073912.959 End of init_database_cache()
13810:20140207:073912.959 In init_configuration_cache() size:33554432
13810:20140207:073912.959 In zbx_mem_create() descr:'configuration cache' param:'CacheSize' size:28521268
13810:20140207:073912.959 zbx_shmget() removing existing shm_id:5275652
13810:20140207:073912.960 valid user addresses: [0x7f1af5c8a170, 0x7f1af77bd328] total size: 28520888
13810:20140207:073912.960 End of zbx_mem_create()
13810:20140207:073912.960 In zbx_strpool_create()
13810:20140207:073912.960 In zbx_mem_create() descr:'string pool' param:'CacheSize' size:5033164
13810:20140207:073912.960 zbx_shmget() removing existing shm_id:5308421
13810:20140207:073912.960 valid user addresses: [0x7f1af57bd168, 0x7f1af5c89cc0] total size: 5032792
13810:20140207:073912.960 End of zbx_mem_create()
13810:20140207:073912.960 End of zbx_strpool_create()
13810:20140207:073912.960 End of init_configuration_cache()
13810:20140207:073912.960 In init_selfmon_collector()
13810:20140207:073912.960 init_selfmon_collector() size:35832
13810:20140207:073912.960 zbx_shmget() removing existing shm_id:5341190
13810:20140207:073912.960 End of init_selfmon_collector() collector:0x7f1af57b4000
13810:20140207:073912.960 In zbx_vc_init()
13810:20140207:073912.960 In zbx_mem_required_size() size:0 chunks_num:1 descr:'value cache size' param:'ValueCacheSize'
13810:20140207:073912.960 End of zbx_mem_required_size() size:427
13810:20140207:073912.960 In zbx_mem_create() descr:'value cache size' param:'ValueCacheSize' size:8388608
13810:20140207:073912.960 zbx_shmget() removing existing shm_id:5373959
13810:20140207:073912.960 valid user addresses: [0x7f1af4fb4170, 0x7f1af57b3ff0] total size: 8388224
13810:20140207:073912.960 End of zbx_mem_create()
13810:20140207:073912.960 End of zbx_vc_init()
13810:20140207:073912.960 In DBcheck_version()
13810:20140207:073912.960 In DBconnect() flag:0
13810:20140207:073912.983 query [txnlev:0] [select oid from pg_type where typname='bytea']
13810:20140207:073912.989 PostgreSQL Server version: 90302
13810:20140207:073912.989 query [txnlev:0] [set escape_string_warning to off]
13810:20140207:073912.990 query [txnlev:0] [show standard_conforming_strings]
13810:20140207:073912.991 query [txnlev:0] [set bytea_output=escape]
13810:20140207:073912.991 End of DBconnect():0
13810:20140207:073912.991 query [txnlev:0] [select 1 from information_schema.tables where table_name='dbversion' and table_schema='public']
13810:20140207:073913.001 DBcheck_version() "dbversion" does not exist
13810:20140207:073913.001 query [txnlev:0] [select 1 from information_schema.columns where table_name='config' and column_name='server_check_interval']
13810:20140207:073913.013 query [txnlev:1] [begin;]
13810:20140207:073913.013 query [txnlev:1] [create table dbversion (
mandatory integer default '0' not null,
optional integer default '0' not null
)]
13810:20140207:073913.018 query [txnlev:1] [insert into dbversion (mandatory,optional) values (2010000,2010000)]
13810:20140207:073913.019 query [txnlev:1] [commit;]
13810:20140207:073913.024 query [txnlev:0] [select mandatory,optional from dbversion]
13810:20140207:073913.025 current database version (mandatory/optional): 02010000/02010000
13810:20140207:073913.025 required mandatory version: 02020000
13810:20140207:073913.025 starting automatic database upgrade
13810:20140207:073913.025 query [txnlev:1] [begin;]
13810:20140207:073913.025 query [txnlev:1] [alter table proxy_autoreg_host alter id type bigint]
13810:20140207:073913.049 query [txnlev:1] [update dbversion set mandatory=2010001,optional=2010001]
13810:20140207:073913.049 query [txnlev:1] [commit;]
13810:20140207:073913.062 completed 0% of database upgrade
13810:20140207:073913.062 query [txnlev:1] [begin;]
13810:20140207:073913.062 query [txnlev:1] [alter table proxy_dhistory alter id type bigint]
13810:20140207:073913.079 query [txnlev:1] [update dbversion set mandatory=2010002,optional=2010002]
13810:20140207:073913.080 query [txnlev:1] [commit;]
13810:20140207:073913.094 completed 1% of database upgrade
13810:20140207:073913.094 query [txnlev:1] [begin;]
13810:20140207:073913.094 query [txnlev:1] [alter table proxy_history alter id type bigint]
13810:20140207:073913.112 query [txnlev:1] [update dbversion set mandatory=2010003,optional=2010003]
13810:20140207:073913.112 query [txnlev:1] [commit;]
13810:20140207:073913.129 query [txnlev:1] [begin;]
13810:20140207:073913.129 query [txnlev:1] [alter table history_str_sync alter id type bigint]
13810:20140207:073913.141 query [txnlev:1] [update dbversion set mandatory=2010004,optional=2010004]
13810:20140207:073913.141 query [txnlev:1] [commit;]
13810:20140207:073913.155 completed 2% of database upgrade
13810:20140207:073913.155 query [txnlev:1] [begin;]
13810:20140207:073913.155 query [txnlev:1] [alter table history_sync alter id type bigint]
13810:20140207:073913.167 query [txnlev:1] [update dbversion set mandatory=2010005,optional=2010005]
13810:20140207:073913.167 query [txnlev:1] [commit;]
13810:20140207:073913.181 query [txnlev:1] [begin;]
13810:20140207:073913.182 query [txnlev:1] [alter table history_uint_sync alter id type bigint]
13810:20140207:073913.191 query [txnlev:1] [update dbversion set mandatory=2010006,optional=2010006]
13810:20140207:073913.192 query [txnlev:1] [commit;]
13810:20140207:073913.202 completed 3% of database upgrade
13810:20140207:073913.203 query [txnlev:1] [begin;]
13810:20140207:073913.203 query [txnlev:1] [update profiles set idx='web.screens.period' where idx='web.charts.period']
13810:20140207:073913.206 query [txnlev:1] [update profiles set idx='web.screens.stime' where idx='web.charts.stime']
13810:20140207:073913.206 query [txnlev:1] [update profiles set idx='web.screens.timelinefixed' where idx='web.charts.timelinefixed']
13810:20140207:073913.208 query [txnlev:1] [update dbversion set optional=2010007]
13810:20140207:073913.208 query [txnlev:1] [commit;]
13810:20140207:073913.209 query [txnlev:1] [begin;]
13810:20140207:073913.209 query [txnlev:1] [alter table triggers alter expression type varchar(2048)]
13810:20140207:073913.210 query [txnlev:1] [update dbversion set mandatory=2010008,optional=2010008]
13810:20140207:073913.210 query [txnlev:1] [commit;]
13810:20140207:073913.210 completed 4% of database upgrade
13810:20140207:073913.210 query [txnlev:1] [begin;]
13810:20140207:073913.210 query [txnlev:1] [alter table httptest alter applicationid drop not null]
13810:20140207:073913.210 query [txnlev:1] [update dbversion set mandatory=2010009,optional=2010009]
13810:20140207:073913.211 query [txnlev:1] [commit;]
13810:20140207:073913.211 query [txnlev:1] [begin;]
13810:20140207:073913.211 query [txnlev:1] [alter table httptest add hostid bigint]
13810:20140207:073913.211 query [txnlev:1] [update dbversion set mandatory=2010010,optional=2010010]
13810:20140207:073913.211 query [txnlev:1] [commit;]
13810:20140207:073913.211 completed 5% of database upgrade
13810:20140207:073913.211 query [txnlev:1] [begin;]
13810:20140207:073913.211 query [txnlev:1] [update httptest set hostid=(select a.hostid from applications a where a.applicationid = httptest.applicationid)]
13810:20140207:073913.214 query [txnlev:1] [update dbversion set mandatory=2010011,optional=2010011]
13810:20140207:073913.214 query [txnlev:1] [commit;]
13810:20140207:073913.214 query [txnlev:1] [begin;]
13810:20140207:073913.214 query [txnlev:1] [alter table httptest alter hostid set not null]
13810:20140207:073913.214 query [txnlev:1] [update dbversion set mandatory=2010012,optional=2010012]
13810:20140207:073913.214 query [txnlev:1] [commit;]
13810:20140207:073913.214 completed 6% of database upgrade
13810:20140207:073913.214 query [txnlev:1] [begin;]
13810:20140207:073913.215 query [txnlev:1] [alter table httptest add templateid bigint]
13810:20140207:073913.215 query [txnlev:1] [update dbversion set mandatory=2010013,optional=2010013]
13810:20140207:073913.215 query [txnlev:1] [commit;]
13810:20140207:073913.215 query [txnlev:1] [begin;]
13810:20140207:073913.215 query [txnlev:1] [drop index httptest_2]
13810:20140207:073913.215 [Z3005] query failed: [0] PGRES_FATAL_ERROR:B??D: indeks "httptest_2" nie istnieje
[drop index httptest_2]
13810:20140207:073913.215 query [drop index httptest_2] failed, setting transaction as failed
13810:20140207:073913.215 query [txnlev:1] [rollback;]
13810:20140207:073913.215 database upgrade failed
13810:20140207:073913.216 End of DBcheck_version():FAIL

Should I give you any data/info from database?