Where are you creating the ODBC connection? In the ODBC Administrator? What type of connection are you creating? User? System? Where are you looking to see the connection does not exist? From another program? Do you have screen shots?
What version of Server 2003 are you running? x86 or x64? In case of x64, then the default ODBC manager from Control Panel is x64 ODBC manager. If you create the ODBC connection here, x86 applications will not see such connection. If you need to use the ODBC connection in x86 application, you have to create the ODBC in the x86 version of ODBC manager. To run the x86 version, you have to launch `C:\\Windows\\SysWOW64\odbcad32.exe`. The same applies vice versa. If you create an ODBC connection using the x32 version of ODBC manager, x64 applications will not see such connections.