That the POP, NNTP, and especially HTTPS all continue working makes me think that it probably isn't the wireless.

Do you have more than one browser on your computer, and if so does it happen with both? If not, it may be some sort of proxy setting in the browser redirecting port 80 (HTTP) requests to a misbehaving proxy application (though, of course, both browsers might be redirected to the proxy app, so the test only works in one direction).

Before chasing down various wireless problems, do you have a regular ethernet card on the computer? If so, I'd drag the computer downstairs (or borrow a really long network cable), connect it to the wire and see how it behaves. You said that the problem happens within minutes, so you could conclusively show that it is or isn't the wireless layer.

-jk