I have a number of nc6000s at our school. I came across this forum looking for the power on problem that is described in this thread. I accidentally found a very strange situation that occurs. This is not a fix, in fact it actually points towards a problem with HP's repair center.
Once this problem occurs, and after it shuts itself back down, if you use the palm of your hand and press down gently on the J-K-L area of the keyboard, then press the power on switch, the units powers up normally!!!!!! DO NOT PRESS DOWN HARD!
Sometimes the unit comes on and stays on, sometimes it is very movement sensitive, sometimes it drops power again in short order. Whichever the situation, it is always repeatable. The very unfortunate part of this is that a replacement motherboard may have exactly the same problem. I suspect that the HP repair facility, not being able to find a problem with the failed motherboard, simply puts it back into the "good spare part" category.
All of my units are still under service contract. On the very first one of these, the unit was out of service for two and a half months while the service technician replaced motherboard, CPU, etc., and ultimately sent it back to HP who replaced the motherboard again. So far there have been six, one arriving on my bench this afternoon. This problem first surfaced after the notebooks had been in service for 22 months.
To summarize, if you purchase a motherboard from anyone at all, insist on at least a 30 day warranty, preferably longer.