(This seems to be a common problem, and there seems to be a lot of confusion about how to fix it, so I decided to post this entry in hopes of helping to alleviate the confusion).
I read something that seemed to indicate that the Antivir Solutions malware gains entry by exploiting a vulnerability in old versions of Adobe Reader, so I looked into my situation and found that I had an old version, and decided to update to the latest, just in case. While removing the old version, I got an "Error 1402," meaning that the uninstaller had been blocked from making necessary changes to the registry.
To make a long story short, I took care of this problem by running regedit to change the permissions on each of the registry elements which caused the installer to stop in its tracks (I would fix one, try uninstalling again, and find another one that needed its permissions changed). (By the way, I'm just an average Windows XP user, not a software engineer, but it seems to me that these particular changes don't require much specialist knowledge.) All I did was follow the path indicated in the error message, rght-click on the file of interest, and select "permissions" in the menu that appeared.
When I looked at the permissions of the offending elements, I found that nothing had permission to do anything to them. So, I added "Administrators" and "SYSTEM" to the list of permissions (there is a button that allows you to validate your entry after typing it in, and I suggest you do that), and gave them full control.
Just be very careful when tinkering under this hood because of the potential to cause major damage to your software installation. I suggest reading up on techniques to recover from registry-editing screw-ups before touching it.