I have an example at the bottom of my scratchpad that I'm working on of using DBI::ODBC to recreate the information a DESCRIBE would yield on most databases(and a non-trivial task in Access)

This may help you see how a connection is made.
for example:

#!/usr/bin/perl -w

use DBI ;
use strict;

#connect to Access file via ODBC

my $accessDSN = q(driver=Microsoft Access Driver (*.mdb);).
        q(dbq=\\\\NWKCPU\\c\$\\SubFolder\\Example.mdb);
my $dbhA = DBI->connect("dbi:ODBC:$accessDSN",'','') or die "$DBI::err
+str\n";
[download]

Your code should connect in a way similar to this. with your network path in the dbq= part. A common mistake is to not properly escape backslashes or dollar signs.
I'm also assuming a Windows computer here because they are the most common type to have ODBC drivers and Access databases.