I would suggest you don't use MS Access for your database, but rather adopt SQLite (DBD::SQLite). Both build databases in stand alone files, but SQLite actually conforms with SQL standards and has a much more consistent set of types. I say this as someone who has (and will likely continue to) wrangled .mdb files. SQLite is free, open source, and widely adopted - for example, it is the backend database for Firefox.

If you decide to stick with Access, I have gotten more mileage out of Jet connectors:

my $dbh = do {
    my $access_db_file   = 'file.mdb';
    my $Provider='Microsoft.Jet.OLEDB.4.0';
    my $db_passwd = '';
    DBI->connect(   "dbi:ADO:Provider=$Provider;
                     Data Source=$access_db_file;
                     Jet OLEDB:Database Password=$db_passwd;",
                    '',
                    '',
                    {
                      PrintError => 0,
                      RaiseError => 1,
                      AutoCommit => 0,
                      LongReadLen => 1024**2,
                    }
                 );
};
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