Either make it a system-DSN, or a DSN for the user the CGI runs under. (Whatever it may be...) For the rest of the discussion, I'll assume use of DBI+DBD::ODBC, only...

You might try to use a DSN-less connection with a connection string for DBI, like:

dbi:ODBC:driver=Microsoft Access Driver (*.mdb);dbq=c:\full\path\to\da
+tabase.mdb
[download]

The full path (required!) for the database must be using backslashes, not forward slashes, as a directory separator.

Oh, and the username/password must be given in the connect call, as 2nd and 3rd parameters — use empty strings if none.