Sorry to jump in so late in the thread, but I just got home. What you are describing is indeed a odd behavior. A cursor should never move by itself (unless you have some program making it do so, like a macro, script, etc.), and even less open random websites and click on links. If what you are describing is really happening, there's a chance that you've been infected with a backdoor trojan, also known as RAT (Remote Access Tool, Remote Access Trojan, call it however you like). In order to check your system for a such malware and get it removed, you'll have to get assistance in the malware removal area, and not here. To do that, you have to post a thread in the Virus, Trojan, Spyware, and Malware Removal Logs
section. You have to follow the instructions in the preparation guide
prior to posting your thread, since it contains the steps to follow when posting it. Once you've been declared clean by your helper, you are free to comeback in this thread so we can continue working on your current issue, if it wasn't solved during your malware clean-up
If you decide to post in the malware removal area, please reply back in this thread with the link to your thread there, so we can get a Moderator to close this one.
On a side note, it's never a good idea to do a System Restore when you are infected with a malware. This is only a last resort solution if you really can't do anything, and even there, these cases are really rare (if you can run FRST from the Recovery PE, a lot can be fixed with it). Also, a Disk Cleanup and a SFC scan won't do anything against active backdoor trojans on a system, even less against suspicious situations like these.
Edited by Aura., 27 May 2015 - 04:19 PM.