I could build you a new one for a small service fee.
If your HP desktop happens to be the one with the NVIDIA GeForce
9300GS graphics card, then it's probably the GPU acting up.
I do recall a particular line of HP desktops with these cards
having all sorts of weird issues. Yours included.
In any case, for your laptop. Use Google Chrome. IE is crap.
Chrome and firefox is just as bad.