hmm. Yea 500W is more than enough to handle that.
Ok, so here is what I would do if I were in your shoes. First, I would boot into windows and download http://www.memtest86.com/ and test your RAM. If something comes back negative I would try replacing the RAM and see what happens Sometimes that can cause weird things to happen. No money spent, no driving necessary, just a little time invested.
If things come back in good working order, then I would try and see if you can return the new PSU and get another one. I KNOW you said it was new, but it could just be a string of bad luck and you might have got a dud. Believe it or not, it happens quite often :/. That would be the cheapest route. If you can't return it, you could probably find an old one at a goodwill or savers or something like that. I Honestly still think its the PSU, but I could be wrong.
If you're still left with the problem, then I would at least try finding a different GPU. This is an easy way just to make sure something isn't goofy with the GTX 750. This is the cheapest one I've seen:
http://www.bestbuy.com/site/xfx-radeon-r5-220-core-edition-1gb-ddr3-pci-express-graphics-card-black/8386085.p?id=1219328762061&skuId=8386085 This is my second hunch and I really hope the problem is fixed by this step.
If that still doesn't fix the problem, you could try replacing the Mobo. get the cheapest one you can find as this is only for testing purposes. If everything works you're golden. Return the "test" mobo and get one of a better choice....unless you like the one you bought.
If shit still hits the fan, then you're going to have to try and replace the CPU, which...there isn't really a cheap way of doing that. Test the new CPU on your old mobo, if it works, great! return the test mobo you bought previously in the last step. If it doesn't work in the old mobo, then you know both the CPU and Mobo were affected. Which means you'll need both replacements.
During this whole process, I would try swapping around the new parts you end up getting with the old parts and playing around to see which is actually the culprit. It could be one thing thats wrong, or it could be 2 or 3. I hope that makes sense.
The absolute worst case scenario is whatever caused the PSU to go out; caused an electrical shock throughout the system which could potentially damage all the hardware connected to the Mobo. This would require all new replacements. I'm not saying that to scare you, I'm just keeping it real.
I personally don't know another way to test a Mobo or a CPU. There might be somethings you could try with a multimeter on the Mobo, but that would require a google search and an answer by someone much smarter than me.
There are MOBO testers that give you an error code to help diagnostic these sort of problems, but I haven't found one with that many great reviews, so it almost seems like a hit or miss.
https://www.amazon.com/Motherboard-Analyser-Diagnostic-Card-Tester/dp/B005J1SUIO
Intel makes a CPU software based test that maybe you could try https://downloadcenter.intel.com/download/19792/Intel-Processor-Diagnostic-Tool. However, I don't know enough about it to give any advice on it.