Right, so I ran the scan, and it was fine. So the other day I thought I'd test the power supply idea by swapping the power supplies between my wife's computer and mine. I took mine out and went to take hers out and everything in her case is cable tied together, I can't take out the power supply without taking out almost every cable or cutting the cable ties. I decided I didn't want to do that so I put my computer back together, after taking the opportunity to take the CPU fan off and brush and clean it out. All I changed was the power cord, I thought I'd try swapping it with a spare.
And the problem was fixed! Game installed and updated fine. No issues at all! So, I assume either I had some loose cables inside and taking it out and putting them back fixed it, or the power cord was dodgy.
And then... it shut down as I was about to start playing the game. But this one was not a mystery, this one quite clearly told me my CPU was overheating. I think when I took the fan off I ruined the connection between the heat sink and the CPU because I cracked that thermal gel stuff. So then I had one of my mated help me put some of that back on and was back in business, no more shutdowns the past two days.
Of course, now my modem is playing up and crapped itself 6 or 7 times yesterday, which is why I didn't post earlier, but that seems ok now... so just waiting for the next thing to crap itself now.
Thanks for everyone's help and if it starts happening again I will just replace the power supply straight up to save time.