Internet is fine. I start browsing, and it goes down. Solution?

Windows 7, 64 bit. Connected through router. Internet works fine. There are downloads and updates going on, no problem. The moment I start browsing, everything goes down and there's no browsing or downloading or any activity. It remains this way for a few minutes then comes back up. It keeps happening over and over again.

I'd really appreciate any help I could get for this strange problem.