You'd do well to follow ColtsFoot's advice. If you haven't set up a datasource, putting the database file (.mdb) in the same directory as the script isn't enough. ("database" NE "datasource") You have to go to "Control Panel > ODBC Data Sources" and configure a driver. If you have no idea what I'm talking about, you should probably read the documentation for DBI::ODBC.

Also remember to use double quotes when you want to interpolate a variable in a string:

1   'DBI:ODBC:$DSN' == DBI:ODBC:$DSN
2   "DBI:ODBC:$DSN" == DBI:ODBC:my_database.mdb
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In your example, you're sending #1 to the database driver, which it isn't going to like, because it has no idea what $DSN means. You want to use double quotes, and send it the name of the datasource, not the name of the variable. Follow?