Random reaccuring problems! trojan?

Befor I had these problems; unable to back out of browser windows, unable to highlight text, opening image previwer caused it to freak out and load every image in the folder over and over..
I installed 3 virus scanners (avg,spybot,norton360) and got my computer cleaned out and all those problems went away.
Then out of no where ‘some’ of my shift keys begin not to work (I had this problem in the past). Then after about an hour (with no software or hardware changes) my shift keys begin to work but my older problems (back button, highlight, image viewer) come back.
Ive also had caculator and browser windows open for no reason by themselves..