Two things: (1) the error message says you're trying to treat a string as a number. ne tests for unequal *strings*, while != tests for unequal *numbers*.

Perl (which, as you're finding out, is Not Java =) provides the defined() function to test for null values. So write that as

while (defined ( my $line = <INPUT>) ) {
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Actually, go ahead and try

while ($line = <INPUT>) {
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as even blank lines contain newlines, and so evaluate to true.

(2) it makes more sense to write parseDown¹ as a subroutine that accepts $filename as an argument than as something that expects a global to be set. Here it's not causing problems but it's not a good design to use in any script you'll keep (or cadge code from!).

sub parseDown {
  my $filename = shift @_; # or $_[0] or just plain shift
  # rest of sub
}
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(3) use strict and warnings (-w in pre-5.6.0 Perl). Doing this will require that you declare your variables with my² and pay attention to scope. This is a Good thing.

(4) don't blindly use $1 and $2 without checking to see whether your regex matched. If it doesn't weird things can happen. Instead, do this:

if (my ($tmp_dir, $file) = $line =~ m%(.*)\\(.*)% ) {
    # do the rest of the stuff
} else {
    warn "$line has incorrect format!\n";
}
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(5) I can't count.

HTH

¹ That spelling, and the != null test, suggest you're coming from a Java background. Apologies if that's incorrect.
²(update) or our (5.6.0) or use vars. Included for completeness. Ignore this for now, I just don't want to say anything false.