Marc, if I were in your shoes I'd back up valuable data and then zap the bloody lot and start over with a re-format clean install of Windows 7 64 bit. Your symptoms sound extemely scary to me and I wouldn't muck about trying to repair things. I trust you don't do online banking as I'd be petrified of key loggers stealing my passwords. Sorry to sound alarmist, but it sounds like you need to regain confidence in your system.
My PC became slow a couple of months ago and although I had none of the scary stuff going on which you describe I nevertheless lost confidence. I keep copies of my important stuff an an external drive, so reformatted and installed Windows 7 64 bit and have never looked back. It was a pain re-installing a lot of music apps like plugins, etc. but the PC runs smooth and fast now.
Sonar X3c Producer
Studio One Professional V2 2.6