Hello, and welcome to PCHF.
First of all, do not pay anything! I know you are smart enough not to do that, but I have seen some people pay to get rid of such nusiances, which is plain foolish.
I'm quite positive that your computer is infected, please follow the instructions in the Prework as Athlon directed and post back with the logs. With any hope, the problem should be fixed; but if it's not we'll take it from there.