|This happens on a lot of these, so this is what I have found to be the problems, could be any of these.|
Memory Slot Failed.
Most of these boards can be repaired by re-flowing the chipset, or replacing the processor. I have found a high failure rate on the AMD chips that are date stamped 2007
But before you have any of this repaired. Lets just see if the computer is locked up. Take out both sticks of ram, then just put one stick in the top slot. With the battery out and off of AC. Press and hold the power button for a minute, now put the battery back in and plug in the AC Adapter. Now try to power it up, if it doesn't work, repeat the process with the ram in the bottom slot. If that doesn't work it's the CPU or Motherboard.
Lots of failures with this model, and most HPs for that matter.