Overall drop in reliability
 

I haven't changed any parts aside from the monitor on this computer in 3 years. And it's really acting up this week. TF2 will corrupt itself on certain servers, Steam is slow and unreliable, firefox is freezing, defragging the computer only made all of the problems worse, and it's had 3 blue screens in 2 days, which is 3 more blue screens than it's had in 3 years. Anti-virus, including malwarebytes doesn't detect anything. I don't know where to start looking for the problem.

I don't know why this is in general hardware, but I'm not saying it can't be a hardware problem.

I see the problems being in Memory, Power Suppy, Hard Drive

One of those three...

I am more keen on

Hard Drive -> Memory -> Power Supply

Run a full error (chkdsk) scan on the hard drive. Run a check on the memory. Do both.

If the behavior persists after chkdsk as Zod has suggested, download and do an error scan on the problem HDD.
Also check the health in HDTune

Here's the link to HDTune site

I'll do chkdsk when I get up, so don't expect any response for about the next 10 hours.

What were the BSODs error message? They usually give a pretty good idea of what is causing it. BSODs are usually caused by failing motherboards or RAM. They can also be caused by the CPU if it is being pushed too hard.

I didn't have auto-restart turned off, so I can't see the blue screen until I get another one.

How long since you did a fresh install? Maybe it's time.

I had the same problem a while back. Turned out I had a bad sata cable. Spent $0.99 and my system is stable again.