Well done.
That looks good, as we have removed memory and hard disk issues. Check disk will try to repeat again on restart where it didn't previously finish, so I am confident it is ok.
When you have fnisished that, please download and run
Malwarebites ensuring you have updated it first.
Its looking increasingly like an issue potentially with your PSU. Old, cheap OEM PSUs do begin to fail, and although I cannot be sure without propoer onsite testing, I would suggest that is a likely candidate. Especially if you are in the USA, where I guess it is summer (reduces efficicieny and makes problems worse), that could be it.
Make sure you have no dust accumulated in the CPU fan.
The other thing I would like to investigate is updating the motherboard bios, however I cannot find any updates for your exact board. You may want to do your own research and post if you find something. This can frequently fix issues like this.
Make sure you turn off sleep mode as this seems to be failing to wake properly (related to old bios i think). But you also told me that it has failed during use, so I still think (based on the fact that the RAM and HDD is good), that you are seeing signs of a failing PSU. I would recommend your Dad considering upgrading to something cheap, but confirmed good as this:
$20 (after rebate) 460W PSU Coolermaster. Its only really designed for computers without discrete graphics cards (like yours), and is likely to be a big step up from what you currently have.
If I were a betting man, I would suggest you have a failing PSU as we have pretty much excluded everything else. Please look at the sticker on the side of the PSU and report the brand and model number. Then do this to be sure:
- Run your Antivirus again - fix issues
- Install and run Malwarebytes - fix issues
- Investigate motherboard BIOS updates - consider calling emachines
- Ensure computer is dust free
- Reapply new thermal paste to CPU (if you are confident in doing this)
- Replace PSU
- Reinstall Windows
Thats about as much help as I can give you. Sorry.