Hi, I think the problem is the open STDOUT. You're redirecting the output of STDOUT to $file, and in fact the select(STDOUT) doesn't acheive anything, because the default output handle is already STDOUT.
Another way around would be to open a read pipe from a system command, like this:

#!/usr/bin/perl -w

use strict;

my $output = "out.txt";

open(OUT, ">$output")
        or die "Couldn't open $output: $!\n";
open(IN, "date|")
        or die "Couldn't open date|: $!\n";
print OUT <IN>;
close(OUT);
close(IN);
print "This gets printed to stdout.\n";
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There are, of course, other ways to do it, but that's something for some more experienced monks to attempt :).