BSOD at virtually random times

About 2 weeks ago, I switched out the power supplies in my computer, as the older one seemingly died. Before, I never had any BSODs except a very occasional one, which I assumed was due to the amount of RAM I have (2GB). After installing the new power supply, I'm getting frequent BSODs.

I haven't narrowed it down to any one thing. It will BSOD if I'm playing a game (not just one, but any game I play has the potential of BSODing that session) and just on the internet. Furthermore, it also will BSOD if it's left idle on the desktop.

I've tried reinstalling windows, but that didn't help. I also tried updating my drivers using the device manager, but because my computer is older, I'm guessing not all of the newest drivers are coming up when windows searches for them.

Edit: Forgot to mention. I've also downloaded Memtest86 and ran for 10 passes without any errors popping up.

I've attached a Speccy screenshot.

Also, I'm afraid my wording wasn't the best. I didn't put a "new" psu into the computer. I had another computer with some hardware (the previous PSU that went dead was under 300W and this one is 350W so I doubt it's a wattage problem directly). That said, It's perfectly reasonable to assume that the PSU is the cause of these blue screens, but I've also attached an updated .zip file containing all DM Log stuff.

I felt inclined to include an updated .zip because there have been more than one BSOD just in the attempt to trying to post this. But it appeared to be varied causes and they certainly didn't happen when any one thing was supposed to have been executed, unless it was done in the background, of course.