For some reason, my previous and new energies are often identical despite moving am atom in space...

Perhaps this has something to do with it?

sub total_energy {
    my $totalE = 0;
    foreach my $i ( 0 .. $#arrayx ) {
        foreach my $j ( $i + 1 .. $#arrayx ) {

            my $r = sqrt(
                ($arrayx[$i] - $arrayx[$j])**2 +
                ($arrayy[$i] - $arrayy[$j])**2 +
                ($arrayz[$i] - $arrayz[$j])**2
            );
            $totalE = $totalE + vdw( $r );
            return $totalE;
        }
    }
}
[download]

You set up nested loops to iterate over your atoms and calculate your total energy, but then unconditionally return from inside both loops after their first iterations.

If you moved the return to the end of the subroutine, it would make a big difference. (It might not totally fix things, but it should help.)