If it is malware and it is attempting to prevent anti-malware scanners from detecting/removing it, I would try to run the AVG scanner
in Safe Mode. Make sure AVG's virus definitions are up to date first.

If that doesn't find it, I would then try both Malwarebytes Antimalware and SUPERAntispyware, and scan with both, one at a time, in Safe Mode.

If the malware prevents you from downloading those utilities, download them and their definitions some other way, eg on a relative or friends' computer, transfer them to your computer via a USB stick, CD, or similar and try installing them that way.

If the malware prevents Malwarebytes from running, find the Malwarebytes executable file, and rename it to anything else, double click that to open and run it.

Just one thing. Are you sure this is a screensaver, and not some issue with your video card?