Actually having just read the pod for DBD::ODBC they have introduced direct access to mdb files since last I looked (6 years ago more or less :-). I think your original code would have worked if you had specified the full path to the testdb.mdb file. See DBD-ODBC/ODBC.pm#Connect_without_DSN

Anyway glad you got it working. As noted in the DBD::ODBC pod if you use the DSN method that worked for you then you need to make it a system DSN, not a user DSN.