Yes, this dialogue in badly translated Swedish (usually a telltale sign of scams) kept popping up and wouldn't go away. Checking the activity handler revealed "absunset" thread running, and we couldn't terminate it.
Googling "absunset removal" proved even worse, some sites containing malicious code appeared (didn't go in to them, but my browser warned) all of them stating "it is *very* difficult to remove manually, but downloading and running our SuperDuperMalwareRemover will solve your problem… (Nope, didn't do that either!)
Rather stupid, but after rebooting, we were able to uninstall everything "ab*" using Windows' uninstaller, and it seems there are no problems now.
I'm sorry we wasted your time, but grateful for the replies you supplied. We will now buy the professional Avast version!