This is true both with IE and Firefox and is even slightly evident on the Windows ME screen itself - so it's a computer problem not a monitor problem - I had the same problem when I tried using an alternate monitor.
I've searched the HP website, Microsoft and Google for causes and solutions but can't seem to isolate the problem. I restored the computer back as far as possible (before the problem) but that didn't help. Any ideas?
run spybot or adaware
Sorry - can't even guess what is causing the problem.
It could be the video card. You might try pulling it out and putting it back in to make sure it hasn't gotten loose. That probably isn't the problem, (a bad card would be more likely than a loose card) but it is an easy and cheap thing to try first.