OK, so my guess is that the problem may be caused by 1) Video Card or 2) Power Supply 3) hard drive. If the problem only occurrs when the computer is cold (which is what I understand from your test results), my guess is that the problem may be caused by 1) Video Card or 2) Power Supply 3) hard drive.
If the problem only occurrs when the computer is cold, which is what I understand from your test results:
1) What type of video card are you using? If it’s installed, you could switch to the integrated video chip, and see if any difference. If it’s integrated, you could try with a PCI/PCIe video card… you can find some used VCs for very cheap prices. I keep one of those for such cases.
http://3btech.net/sp8425pciexv.html
http://www.pricewatch.com/video_cards/
If you already have a PCI/PCIe card installed, switch to the onboard video chip in the Control Panel\Display, and next shutdown the computer, switch the cable connector, start the computer and enter the BIOS and switch the setting to the onboard VC. If no restarts are necessary after a few days, the video card was the cause… check it’s firmly seated in the slot, clean the pins and slot or replace the card. And if there is no difference move on to other hardware as the likely cause.
2) The shutdown and new restart test may mean the PSU is not providing full power. I experienced a similar problem with an old computer… the PSU apparently didn’t produce enough power to spin-up the Hard Drive fast enough on the first startup.. I replace the Power Supply and problem solved.
3) Another time the hard drive didn’t spin-up all the way on the first startup… it needed more time.. it also had glitches during normal operation, sometimes it made a single barely heard click, and the screen sort of twitched. it was the Hard Drive. I’ve found a good application to read the Hard Drive condition… it’s Hard Drive Sentinel, it reports power on times in days and estimated remaining lifetime in days. It also reports performance and health in percentages, and a temperature and S.M.A.R.T. reports
On the Minidumps, do a file search for minidump or for ".dmp" files because minidumps can also be located in the All users profile.
You can also look in the Event Viewer in case it has registered the problem. Right click on the My Computer icon, and select Manage\Event Viewer.. see if any events were registered at the exact time of a black screen.