I had one of the HP dv6000's that began to have screwy shutdown and reboot problems. Turned out to be the video card dying. I rejuvenated it once by disassembling the laptop and applying a heat gun to the video card, then replacing the original heat paste soaked fiber with a copper shim. But that fix only lasted 6 months and when it began again, I sprang for a new lappie, feeling extremely fortunate to have successfully reassembled the unit once. I'd had the unit for six years and after Googling the unit, considered myself lucky for it to have lasted that long. Seems that model is rife with spooky hardware problems. The problem began after installing a particularly video intensive game. Don't know if this applies to you but PCLOS 12 may be more stressful than prior versions. Since it is a fresh install you should have no critical data at risk but if you do, back it up now.
Maybe it is a software issue. God knows there are plenty of opportunities. Good luck.