Check your system using any of these programs (I reckon using all of them):
http://www.lavasoftusa.com/software/adaware/(free) http://www.grisoft.com(good free AVG) http://www.ewido.com(>>now called AVG Anti Spyware<< free 30 day trial -the best in my opinion) http://www.ccleaner.com/download/(free) Spybot - Search & Destroy (FREE)
I would start with the CCleaner, just to make your old computer run a bit faster.
Then go hard core and use the AVG Anti Spyware, afterwards the AVG Anti Virus and then, just to make sure, AdAware and Spybot. In between do always reboot after each cleaning process....
And when you're done with the first round, use AVG Anti Virus on more time, just to be on the save side....them you can start to transfer your files...
