Nice to hear that your AHT problem is solved, but I'd love to know if unplugging the router would have worked.
Under any circumstances, though, you should always keep unplugging the router in mind as a potential fix for any sort of Internet connectivity problem.
Assuming your Safari 6.0.5 works similarly to my 10.1, yeah, every open tab eats its own ration of RAM.
It sounds like tacit is right on the mark about insufficient RAM despite the fact that Apple deemed it sufficient when they set the specs for your MBP, and you'd really do yourself a favor upgrading from 4 GB to 8 GB, but you can try closing tabs and unnecessary apps to see if it helps enough to get you by.
