Well that's quite a pickle. My mum had one of these and McAffee didn't even recognise it. She then ran Windows Defender, which I think is free from the MicroSoft site (or at least it was), and that found it and got rid of it. If that doesn't work, another free one is SpyBot Search & Destroy, though I haven't tried that out myself. So give those a go.
Even if you did have to buy some software, don't buy it on the computer you're on, otherwise the keylogger would have all your details and everything. Sorry if that sounds really obvious, I'm not trying to be patronising.
Hope that helps.
EDIT: got some links for you DefenderSearch & Destroy