First, your commented if clause would work if you changed your "or" to an "and" - a valid choice must be both not "." and not "..". Also, in regular expressions, . is a wildcard character, so they will match far more than you intend - see perlretut.

If you wanted to avoid some layers of conditional nesting, you could use next as a short circuit on your file tests. Something like:

opendir(GPS,"$new_dir") or die "Cannot open directory";
my @GPS = readdir(GPS);
closedir(GPS);

foreach my $kid (@GPS){
    next if $kid eq ".";
    next if $kid eq "..";
    next if not defined $kid;
    next if $kid =~ /\.bak$/;
    next if $kid =~ /\.txt$/;

    open KID , '<', "$new_dir\\$kid" or die "Open failure on $kid: $!"
+;
    my ($dev,$ino,$mode,$nlink,$uid,$gid,$rdev,$size,$atime,$mtime,$ct
+ime,$blksize,$blocks) = stat(KID);
    my $data = <KID>;
    close KID;

    if (defined($data)){
        my @data = split(" ", $data);
        my $diff = time-$mtime;
        if ($diff >= 3600){
            unlink($kid);
        }
        elsif ($diff >= 20){
        }
    }
}
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Update: I forgot to mention you should be checking whether open succeeds or not. As well, you may consider checking out the file tests available in -X.