Once again, I have posted the wrong solution. The above solution will give you a time difference if you subtract here from there. However to get the equivlent there time for a particular here time, do this:

use DateTime;
%OurLogs = get_the_time_from_the_log_file_as_a_hash();
$here = DateTime->new( time_zone => 'America/Indiana',
                           map { $_ => $OurLogs{$_} }
                           qw( year month day hour minute second ) );
$there = $here->clone;
$there->set_time_zone('America/Los_Angeles');
[download]

This will give you the equivlent time in LA for the time in Indiana. Please note that you should set the timezones to appropriate values :)

Many appologies for all the confusion. I woke up at about 3am in a cold sweat realising that I'd posted the wrong solution :)