High-pitched noises during dskchk, corruption on fresh Win10 install

(full disclosure of my journey ahead, relevant info may be limited to the last few paragraphs)

My desktop wanted to restart last night, so I let it. "Getting Windows Ready..." It said, for 3 hours. Enough is enough, so I broke the rules and powered down. Obviously BSoDs ensue, but it's fine, Windows is on an SSD with just a few video games on it, all my files are on a separate HDD. System restore fails, reset this PC fails, lots of corruption, gets worse every reboot... eventually it fails to boot and then just boots to an unchanging grey screen, so I make a USB stick and reinstall Windows 10 Home on the drive, and scrounge my product key out of Windows.old...

Interestingly, the BSoDs don't necessarily stop. Mostly MEMORY_MANAGEMENT, with one KERNEL_DATA_INPAGE. That last one points to bad RAM, so I test that with Windows and it comes out fine. Now I suspect is the drive, but I got Overwatch installed just fine, so maybe everything worked itself out? (lol)

I've tried DISM and SFC a few times, SFC finds issues but can't fix them all, DISM also finds issues but doesn't have a source. I can't find an install.wim file or even a guide on how to get one. I tried pointing it to my install.esd file on my USB boot drive I made, but it still didn't work, and since I'm on Win10 Home, I seemingly can't access group policies to modify DISM behavior like some guides said to do.

Soon after, all my chrome extensions are breaking and every page gets an "Aw snap!" after a moment or two. I reinstall chrome and disable all extensions, fixing this until I restart again. I try to download League, and I get the client installed, but it keeps throwing error 004, failed to patch when downloading the game.

Eventually we get to where I am now, in the middle of a CHKDSK C:, stuck at 11% for the entire time I've been writing this post, with a concerning high pitched noise coming from my tower. My C drive is an SSD and people will argue that with no moving parts it can't make noise, but surely it's not either of the HDDs, since it's only checking the C drive.

What else could this noise be? Is it my SSD, or another component? The test for the RAM said it was fine, but is it possible that it was wrong?

PRE-POST EDIT: Right at the end of this writing, after 10-15 minutes of being stuck at 11%, the tower went from the high-pitched wail to a single, higher-pitched beep, restarted, dskchk showed up again briefly but at 100%, and then it brought me to my login. Chrome runs, OW runs, discord opened, then crashed and opened to a gray screen until I ran it as administrator. League closed abruptly when I logged in, then let me log in when I ran as administrator. My computer has been making a rattling and intermittent whirr since rebooting, sounding like a metal fan that's slightly off-balance or something, and then going away for a bit. No more high pitched sounds since DSKCHK ended... The whirr went away after a few minutes of being on, and League hit error 004 while patching again, at ~20% (much further than it usually gets)

I really want to get this fixed ASAP since my school term begins before long and I use this desktop heavily, so any help would be appreciated.

It seems like a hardware issue for sure, since I performed a clean install and it's still acting up, however I don't have a good way to determine which piece of hardware is acting up. Also, despite being a CS engineering student, I know extremely little about the hardware side of PCs. I'm a poor college student, so I'd rather not just throw money at replacement parts until I find the correct one.

I'd appreciate any help I can get.