You haven't provided much information.
Given that you've posted this in the ODBC forum, you are indeed using ODBC then?
Are you able to connecting using the same ODBC DSN and clicking the "test connection" button in the dsn config applet?
Are you able to connect without odbc? Using SQLPlus for example?
12504 generally means your tnsnames.ora entry is wrong, and your dba should be able to help you out with the proper information for the entry.
Hope it helps,