Just check to see if the uppercase version of the file name is in existence already (or the same as un-uppercase version), print a message if so, and rename the file if not. I wouldn't personally try doing this in one line.

use strict;
use warnings;

my ($old, $new);
my $dir = "/u/web/hom420/test/";

die "Directory $dir does not exist" unless -e $dir;
die "Directory $dir could not be opened" unless opendir(DIR, $dir);

while ($old = readdir(DIR)) {
    next if -d $dir.$old;
    next if ($new = uc $old) eq $old;
    if (-e $dir.$new) {
        print "Collision: $old -> $new\n"; next;
    }
    rename $dir.$old, $dir.$new;
}
[download]

NOTE: This is not a recursive solution. It also doesn't work on a case-insensitive OS - something like MacOS will need a more imaginative solution.