I've installed Avast and I'm running it and I'll post a HJT log once I'm done but I think I've actually solved the problem. Spybot S&D seems to write all these spyware sites into the "hosts" file in C:/Windows/system32/drivers/etc folder so that if your computer tries to connect to them it goes to 127.0.0.1 instead. I edited the file and my DNS cache is normal and my connection speed is back to normal as well. Now I'm wondering if that means that my computer was constantly trying to connect to these all the time?
In any case, I'll post the HJT log again soon, thanks very much for your time!