Restore second-hand computer help

I recently traded a friend for his computer. Its an Alienware X51. He said I only needed to get a antivirus and it would work fine. Turns out the virus is a lot more intense than he let on. It makes normal system restores practically impossible. It also has somehow managed to lodge itself somewhere in the system, so that even when it is removed by the antivirus, it will re-appear in a few days. Now, because I bought this from a friend, I have no windows discs. He also didn't create a point to restore to factory settings. I want to do a full wipe while leaving the OS intact if possible to avoid, naturally, having to pay to but another one. Any help would be appreciated.

some extra info on the virus...

-It has the capability to change settings in antiviruses. I have tried two different antiviruses. AVG and Panda. It will turn off the antivirus and create errors if you try to run a scan. I have used a cloud cleaner through panda, which will detect and eliminate the virus.... until either A. the computer is shut down, logged off, or restarted or B. a time of about 8 hours passes.

-Not effective in safe mode, but can still stop restores while in repair mode. (F8 at BIOS)

-Slows all computer activities while windows is regularly booted. Almost to a halt. Takes about 10 minutes for control panel to load.

I'll definitely post up there as well. As for the F8, it doesn't give me an option to restore to factory settings without a disc to do so with

More about the "factory restore": There's 2 things one can do, one is during the setup or maybe later create the factory restore discs [or USB Thumb/Flash drive] and the other is to determine which key to press to get to the usually-hidden partition on the HDD to start the process, may be F10, F11 or F12. There's usually also a procedure to be used when booted into Windows to do the factory restore. Different OEMs do it differently. Names of the processes may be a bit different, have even seen a CD/DVD burning program have the capability to do it. If that restore partition has been deleted it's back to having the discs or contacting the OEM to order them. Or if not wanting all the 'bloatware' associated with the factory restore buy an OEM or Retail disc which should have a Product Key with it.

Yeah that's the big problem I have. Not sure how to locate the owner to transfer ownership either. My brother never transferred it to himself. And has no way to get in contact with the person who he bought it from. Can Dell contact the person on record to have it transferred that way?