Ack! My computer is crashing mid-game and sometimes doesn't power on! I need help!

Good evening, ladies and gentlemen. I'm not sure if this is the place I should be asking this, however, I've recently run into some issues with my computer. It's run perfectly fine since late 2013/early 2014 up until this past week.

My setup:
PSU Corsair RM850
CPU Intel Core i5-4670
CPU @ 3.40 GHz (4 cores)
GPU GTX 780 Ti
Win 10
Ram 16GB

And recently I've been experiencing crashes while playing various titles on steam such as PUBG and R6S. I'm not sure if this is a power supply issue or a motherboard issue. I've also been experiencing turn on/boot issues, however my motherboard was still receiving power despite my computer not turning on. (Had the green light.) So I tightened power supply connections to the various parts and now it boots alright.

I was wondering how I can get my computer crash logs and if anybody could help me figure this out? I believe my computer is overheating, but it's only done this recently. (I downloaded RealTemp and it reads Min temp 40 and max temp 61 C while on desktop with no open applications aside from Discord and this on Google.

Any help is greatly appreciated! Thanks

NOTE: It doesn't fully crash, in turn it simply freezes outright and requires a restart to do anything.

http://speccy.piriform.com/results/W5papNil7aNq2TY18TQisSg

It also says that my motherboard is 120 C....

That temperature gave me a scare so I restarted my computer, took a look at the BIOS settings and it says that my CPU is @ 36 C and my MB is 24 C. The CPU temp is a lot different than my real temp. https://postimg.org/image/f3i2ynw3v/

Also, you mentioned hard drive.. https://postimg.org/image/b74r2zvsb/

Also, NOTE: My computer is very loud and noisy, and has been for awhile.

My apologies! I'll edit/continue off of single comments. Something worth noting.. I believe my motherboard is sending false temp(s).