Could it be my RAM?

Actually, this could happen because of many reasons. It could be RAM, but it also could be PSU, motherboard, GPU and even HDD/SSD. Only way to be sure is to change components one-by-one, but obviously it's not that easy because you need something else to put instead, and that's a problem if you don't have a "donor" PC (like, one from your friend or something). You can try running tests, like memtest86 for memory, OCCT for GPU, CrystalDiskInfo to check SMART of HDD/SSD, etc... but that's not guaranteed to help you to narrow down the problem (worth give it a try nevertheless). You can also check your motherboard visually, if you see bumped (or even cracked) capacitors - that's probably the cause. Same goes with PSU, but it's harder to disassemble to inspect. Anyway, I wish you luck with this issue, I know how frustrating this could be when PC does not work properly...

bump, hope you find a solution

Don't forget to check you HDD. I was getting hangs and freezes and had to change it.
GPUs can crash into white noises or your screen blinks and memory usually gives fatal errors like blue screens.
Try to boot an OS through USB and see what happens.

Just to share my own experience, crashing while watching videos or playing games was attributed to the GPU. Though my GPU (6600XT) was recently acquired, it was relatively new (bought from someone else). It was still in warranty but I tinkered with the connection by switching to a different PCIe slot (my mobo got 2). And it worked. Did a GPU stress test using Furmark and all was well. Though every time I move the pc or even just unplug the cable, it again crashes and again I reseat the gpu to the PCIe slot. Seems like a connection issue though it happens intermittently and I simply unplug and plug it even on the same slot. Just putting this in, in case you want to rule all possibilities other than the RAM

Bump. I had this happen to me once and it ended up being my power supply.
But since yours does not shut off. It's something else.

How many sticks of ram do you have? I would recommend removing one stick first.

Hope you find and fix the problem, PSU in my opionion is the most important for longevity of other components. I remember you could always check ram with some tools you could boot from pendrive for example but faster way is to connect other memory to test..