Sorry for the delay, this forum is very busy.
I don't see any signs of malware in this log. I see BitComet which is dangerous, like all Peer-to-peer file sharing programs, but it is not malware itself.
My computer has suddenly decided to freeze at the BIOS screen
Let's just make sure about this. The BIOS screen is a bunch of white text on a black background. You see it when you first power on the computer. First you see it counting up and testing your memory, then it starts listing all the devices on your computer -- disk drives, network and sound cards, and so on. Finally it looks for a boot record on one of your drives. Does the computer freeze while this series of steps is going on?
I have had it reformatted 2 times
And did this provide any relief at all or change the behavior in any way, even for a little while?
Please answer these questions so I can recommend some further steps to diagnose this.