It's good that you are testing the return values of each call, and dying when a critical error occurs is generally a good idea. But in this case you don't want to actually die, as this also prints to STDERR - you just want to exit. For example,

eval {
    copy($fileOne,$fileTwo) or die "Failed to copy $fileOne to $fileTw
+o - $!";
};
if ($@) {
    # Record the log information in here
    exit 1;
}
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My personal preference when developing on windows nt/xp systems is to use the event log instead of a log file. I have had good luck with Win32::EventLog::Carp.