Why the restriction on modules? Do you mean without using any modules? Because with Time::Local (part of the standard perl distribution since forever) you can do this:

my $date = "2004-06-14 13:34:54";
my ($year,$month,$day,$hour,$minute,$second) = $date =~
   /^(\d{4})-(\d\d)-(\d\d)\s+(\d\d):(\d\d):(\d\d)$/  or die;

$gmt = timelocal($second,$minute,$hour,$day,$month-1,$year);
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Chop up the date string however you please.