An engineer solved the problem last February. But he is not an HP employee and HP techs still have no clue that there is a solution, even though it is on the HP support forums. So tomorrow I mail my computer to HP again and hope that they will follow the solution. The difficulty is that solving the problem is not exactly their job description. They are supposed to follow a preset algorithm, do various tests, and try stuff.
Last time I sent the computer to them it was over 20 days before I got it back. The problem did not recur until a month later, but it built over time and now it's paralyzing me for longer periods of time. I could just take the computer apart and fix it myself--it involves taping some stuff to shield from static. But that would void my warranty, so if my motherboard fries next week, I'll be out of luck.
I am not optimistic.