So far, disabling that option seems to have done the trick... but you never know!
As for other internet-using programs, I don't really think that is the case. Firefox'll lock up when I'm not running anything else, and other browsers never do, so I'm fairly convinced that it's an issue with the program itself. I've been Googling, and I'm not the only person to encounter this problem; unfortunately there is no posted solution. I'm guessing it's a problem with the most recent version of Firefox, or with my BT connection at home. Restarting the router hasn't helped, so I might give BT a call and see what happens.
Thanks for all the help so far!
Edit: No, it's still happening.