The same situation. Spontaneous reboots were previously observed first once a half-year, then once a month, a week, a day... 
RAM was tested (by the Memtest 86) and showed a lot of errors followed by the system hang up. Replacing the RAM gives no result. It was also observed, that sometime system boots in Windows, but hangs up upon any activity started.
HDD was checked - OK. Now it works fine in a different PC. Among the suspects are motherboard and PSU (power supply unit). OS (Windows 7) required re-activation, however. Compaq was a part of Agilent 7890/5975C GC-MS System.
Dear HP Support, how can MoBo be tested for operability?
Is such MoBo available as a spare part? (HP Compaq 8000 Elite SFF, LGA 775, Q45) 8000E8S Euro.