I don't have ActivePerl installed here at work, but other than the fact that 'LWP::Simple' should be 'use LWP::Simple;', this code works fine under Perl on Linux. I just ran it here, and got the homepage for www.perl.com, as one would expect. I copied your code verbatim.
You might try another page somewhere, maybe on a local server. Also check to see that you have the most recent version of libwww installed. Other than that, I don't see any reason it shouldn't be working.