Well this is really, really odd. I've been busy for the last week studying for an MCDST exam. Decided to run Bearshare today, and... it's working!!!!
I haven't changed anything in the options. All I've done is install some unrelated software, e.g. Speech Recognition - nothing that needs to connect to the internet. Windows firewall is active.
Well, I wish I could tell everyone what happened to fix this so that if someone else had the problem it would help, but I don't have a clue.
Must be another Microsoft feature