Hi there,
are you on PC or Mac?
Do you have a facebook account?
I'm on a Mac, so I know Macs much better than PCs... On Mac, since 10.8, you can link the facebook account, by setting it directly, so you receive notifications directly on the Mac, even without the mailbox open. I could imagine that if your PC is waiting for facebook, it could be a lead? Maybe your password is not registered correctly. However, I doubt that this is the cause of your PC's slowness. Eventually, it could slow down your internet connection...