There are 2 errors in your code: a syntax error '$pattern = \b\w+\b;' and a logical one. Try this:

my ($count,$pattern,$file) =
  ( 0 , qr{\b\w+\b} , shift );
# declares and initializes the three variables
# see perlop for qr//

open FILE,$input or die "Error: $!";
# please read `perldoc -q 'quoting.*vars'`

while(<FILE>){
   $count += () = /$pattern/g;
   # that's kind of an idiom for counting the matches
   # it forces list context on m//g, but forces scalar
   # context on the resulting empty(?) list
   # that returns the number of elements that were
   # assigned to the list, although
   # in the end it's all thrown away, never reaching any
   # accessible memory outside the perl-internals...
   # -- it counts the number of matches
}
close FILE;
[download]

HTH

UPDATE: yes, qr// instead of qx//, i mixed 'em up, because i don't often use qr//. Thanks to sauoq and wog