IC3, 1GB of ram should be completely fine in most any system. Unless you are running some huge apps you shouldn't even be filling up 512MB.
http://free.grisoft.com/ <-- Head over there and pickup AVG anti-virus and get installed. Run a full scan, because it seems as though you may have picked something else up. (caution, some javascript there seems to be making my browser unhappy, so it might make your computer slow until you finish downloading it).
Poorly written spyware is also an option as to what is giving you problems, but I'm a little out of date on what the latest and greatest of the anti-spyware software is. (I'm a linux guy myself.)