Just bought a second hand PC, seems riddled with malware

I bought it under the pretenses that it had malware on it previously, though the former owner believed they had removed it. They had not.

As always, I started off with CCleaner and mbam - only found click potato, thought I was safe.

When browsing later (nothing out of the ordinary, BBC, reddit - that kind of thing) I was told by MSE that it had encountered 'TrojanOS/Alureon.A'. I proceeded to follow the guide in the forum, then the READ ME, and here I am. HitmanPro and Rogue Killer both came up with something. I have followed every single instruction to the letter.

As for performance issues, it seems fine when browsing, but Windows Update has been disabled entirely, and the PC is thus running Windows 7 with no updates at all. Yep, I know. BIOS is password locked (I'll sort that out later if needed). I'm hoping to have all solved so that I can do a nice cheap upgrade to Windows 8.

Thanks in advance - I can tell you're some great guys, so I know you'll get around to me sooner or later.

HP.