Your problem here is not due to CGI.pm. while does not set $_. Plus I think you're forgetting to get rid of the newline. Try this instead:

   while (chomp($_ = <FILE>)) {
      do stuff;
   }
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Update - I'm crazy. while does set $_, but I customarily chomp in the fashion above and I guess I forgot why. :-(
if ($user eq $q->param('ueq &encrypt_pass) {

The above code shouldn't compile. The foreach after it is also completely unnecessary (no sense looping over 1 value). Maybe it ought to look something like:

my $user = $q->param('username');
my $pass = $q->param('password');
verify($user, $pass) or die "No user or password incorrect";
sub verify {
   my ($ck_user, $ck_pass) = @_;
    open FH, $user_file" or die "Can't open file, $!";
   while (chomp($_=<FH>)) {
      my ($user, $pass) = split '\|';
      if ($user eq $ck_user) {
        if ($pass ne crypt(ck_pass)) {
           return 0;
        }
        else {
           return 1;
        }
      }
    }
    return 0;  
}
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Adjust the return values to suit the logic of your program. I assume that at a minimum you might like to know if the user exists in the user list and whether or not their password is correct.