Abigail,
I wasn't going to reply because I have a sum total of 0 experience with socket/network programming. Since other people have wagered guesses and possibilities - I will too:

From the documentation, which I know you said you read, the example that looks most similar to yours is a bit different:

$sock = IO::Socket::INET->new (
    PeerPort  => 9999,
    PeerAddr  => inet_ntoa(INADDR_BROADCAST),
    Proto     => udp,
    LocalAddr => 'localhost',
    Broadcast => 1
) or die "Can't bind : $@\n";
[download]

In particular, the information concerning the peer. I am wondering if setting the PeerAddr to the broadcast does something special even though technically what you have should be picking up from any address. Unfortunately, I do not have the means to test presently.

Cheers - L~R