About the fan, yes, you’d better get it repaired quick.
About the formatting, well I’ve been facing such problems since a long time, and I’ve found two things that work. One is called Bart PE which is some kind of Windows pre-installation thing. The other is Puppy Linux. I don’t know if you’ve used Linux earlier, but this one is really a piece of cake. You can download it from their site, its just 100 MB, then burn to disc (if that’s possible for you with the present state of your computer), and then boot from the CD, and the Puppy will load into the RAM, and you will be able to access the hard disk, and you can also take out the Puppy CD and pop in any other disc because its running from RAM.
Just out of curiosity: how did you manage to get so many trojans that they brought down your computer? What names does your AV throw at you?