Had a couple viruses and now my computer is slow.?

My computer is fast usually. Its a HP dv4 64 bit windows 7 laptop. Dual core 2.10 proccessor, 4GB RAM. Internet has been slow lately period but then I got attacked with viruses Worms and Trojans and made it slower. AVG pro cleaned it up nicely and I installed Ad-Aware free to help clean up any leftovers. Now both full scans say no viruses and I successfully restored to a point before I contracted the viruses. But now internet is somewhat slower than it was. I do not want to Restore to Factory settings because I have alot of stuff on here and not enough space to put it on a flashdrive. 50-60GB in in movies, television alone. 2GB music, and work and school stuff. I am poor so I cant buy a external hardrive. What are the chances of AVG pro and Ad-aware telling me there is no virus when there really is. Computer process seems great. For instance on most peoples computer, Control Panel would take 2-3 seconds to come up. Mine comes up in less than a second when clicked. Just the internet Mozilla Firefox is slow. My moms internet is faster and she has a crappier computer than I do. She uses Google Chrome.