There's a typo in your $DSN assignment where you swap ; and " - I can only assume that means you typed rather than copy/pasted your handle. Try this and see how it works. Note that to avoid escaping errors, I set a file name separately from my driver specification.

my $filename = 'Z:\\temp\KernelLog.mdb';
my $dsn = "dbi:ODBC:driver=Microsoft Access Driver (*.mdb); dbq=$filen
+ame";
my $dbh = DBI->connect(    $dsn, '', '',
                        {
                            PrintError => 1,
                            RaiseError => 0,
                            AutoCommit => 0,
                        }
                    )
    or die "DB connect failed $DBI::errstr.";
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As a coincidence, I am just now migrating an Access database to Oracle. An Access database with non-alphanumeric table and column names. Oy.

Update: Your issue appears to be that your driver specification requires a space between Driver and (*.mdb).