Different BSODs, Hard freezes, random restarts

I've updated all the drivers I could think to. I've replaced the graphics card with no effect, and I've used the memory diagnostics tool. It has given me no errors. I've swapped around RAM, and I've removed dust from inside of the tower regularly. A health check reports no errors with hardware, and Microsoft Security Essentials (fully updated) assures me that I do not have any viruses or malicious software/files. Despite all this, my problem persists and I don't know what to do.

I get Memory management and IRQL not less or equal BSODs pretty often. My PC also randomly (or seemingly) restarts, and it tends to give me a blue screen when I run a game (but I also gives a blue screen randomly or when no one is interacting with it for a while). Sometimes my PC will run just fine for a day or two (or even a week), but the problem will come back and I have no idea what is causing it or how to prevent it.

I'm not extremely tech savvy, but I've done what I can and I have no idea at this point. The PC (which I am posting this from) has restarted or given a BSOD on me several times as I tried posting this. I would greatly appreciate any help.

Is it okay if I bump the thread? I'm new, so I'm not sure... Just making sure I'm not under the radar. I apologize if bumping this is against a rule.