1000W PSU should be more than enough unless you have something huge you are trying to power even a GTX 1080SLI GPU only requires you to have a 900W PSU. I think you may have a short somewhere on the motherboard by the south gate. It could be a micro-soldering repair. Or you may need to buy a new motherboard. You can test my theory by using an alternate motherboard (if you have one lying around). Plug everything, into the alternate motherboard, that you were attempting to plug into the motherboard in question. If it works then the problem is definitely a short on the motherboard and you should repair or replace the motherboard.

It is not difficult to replace the keyboard. The link below is a keyboard that should work for your MBP model. If you need help putting it on post here and i will try and respond quickly. (You can copy and paste the link into your URL Bar at the top and it should take you to the keyboard aforementioned on amazon) https://www.amazon.com/Padarsey-Replacement-Keyboard-MacBook-13-inch/dp/B01M03H4HO/ref=sr_1_1_sspa?ie=UT...-1-spons&keywords=macbook+pro+13inch+late+2...

Thinking a little more about your problem I think you may want to check that the cpu fan is working first (is there an over heating problem?). They are usually pretty cheap and relatively easy to replace in comparison to the hard drive.

That is a hard issue to walk someone through on a message board. Off the top of my head I would say manually pull hard drive and use another computer (I use a hard drive dock station as long as it is a sata connection and not an ata) to copy documents and media you don't want to lose. Then you are going to have to erase the Hard Drive and re-image the OS to the Hard Drive and make it bootable using a bootable usb. Then you will still have to figure out how to activate the OS (different depending on what version of windows you have/want). If you are familiar with bootable usb's and Linux OS's then you can try and run Ubuntu (or other Linux OS) on usb drive to diagnose the internal hard drive before pulling and re-imaging. That requires a little more computer "know-how".

Need to troubleshoot it. Does it boot into OS before turning off? Is it plugged in and/or charged when it "shuts off by itself"? Also are you sure it isn't sleeping?