Lets assume you run WinNT:

I. In BOTH OEM database server and Client:

1. search your disk for tnsnames.ora files

Then: a) either use TNS_ADMIN registry key to use only one tnsnames.ora file (this key must be in ALL oracle homes)
or b) correctly add service name in found and RELEVANT(sample tnsname.ora is not of concern :-)) ALL tnsnames.ora

2. Test connection by using tnsping:
a) cd to <OracleHome>\bin for ALL ORACLE homes you installed (Oracle homes can be found in registry under HKLM\Software\Oracle\Home<ID> and ALL_HOMES, etc, take a look.)
b) run tnsping or tnsping80 from THAT directory.
NOTE: Oracle mixed names of tnsname under windowses:
SQLNet had tnsping.exe
NET8 had tnsping80.exe up to oracle 805
From Oracle8i (815, etc) it is again tnsping.exe
Similar consideration for location of TNSNAMES.ORA file:
SQLNet <OraHome>\network
NET8 of 805: <OraHome>\net80
NET8 for O8i: <OraHome>\network