I have to admit that what you've described has thrown me off balance a tad. If it had been either FF or IE (but not both) then obviously there was scope for a re-install or repair option for the appropriate browser.
The only thing I can think of that is common to both, is the fact that you go online. I suppose there is a vague chance of it being tied up with a virus checker (or some other common factor) that is causing this.
So, I'm scratching around in the dark a bit. All I can suggest is that you disable your connection (probably a tray icon) then repeat the test. If that makes no difference try tempoarily disabling your virus checker. I'm looking for something that will give the necessary lead and can then be tackled.
See how you get on but keep an eye on this post to see if anyone else thinks of something that my head hasn't yet got around to.