I've had many different BSODs randomly, and I'm at wit's end.

I got my new IBUYPOWER machine back towards the end of March (after ordering it at the end of Feburary). Since about Mid-April, it has randomly BSOD anywhere from one every other day, to five times a day. I've spent the last three months trying to troubleshoot it down to a specific part or drivers, with little success (up to and including formatting and using a new HDD, which meant I lost the Office stuff I paid extra for). I have also noticed that it tends get rather hot (like, the side of the actual machine gets VERY hot to the touch - I could fry an egg on the side if I were so bold), even though it's in a well-ventilated area (which leads me to believe that at least part of it is shutting down to prevent overheating). I have attached my .dmp files as well as a log of the error window that pops up. I don't want to send it in because last time I had to wait an entire month for it, but on the other hand, I'm tired of having problems with something for almost the entire time I've owned it.

I've tested with MemTest86 and got no errors. I've turned off Driver Verifier and turned it back on, and I've even used "BlueScreenView", and it shows issues with "NT Kernel & System" on 8/11 of the minidumps, but again, nothing overly concrete.

In terms of heat, I think I am just going to get an extra fan, since I currently have a desk fan on, and it's helping keep cool.

Unfortunately, the short-lived support hours perfectly coincide with my work hours, so I can not call in and request a claim. I posted a request for an RMA on the Customer Support board, and it was suggested that I post here, so I'll jump through one more hoop for this thing.

...sorry, I'm a little bitter. Any help would be greatly appreciated.

Edit - Added the SF Diag Tool results as well. Currently installing virus scan again.

Try disabling hibernation for now.
Hibernate - Enable or Disable
The errors are all over the place. However, it seems the system hibernation function is in play I'd like to get it out of the way for now.
It wouldn't hurt to do a full scan with a antivirus tool either. As malware can sometimes cause stuff like this.
You can use the free version of this tool if you don't have anything available.
Malwarebytes : Malwarebytes Anti-Malware PRO removes malware including viruses, spyware, worms and trojans, plus it protects your computer