I doubt this will help, but maybe some troubleshooting steps. And, it makes it a little more difficult given the multiple versions.
So, looking at the download site, it does state to make sure all Windows Updates have been installed. Probably already been done.
What happens when you install 9.1 on one of the "bad" computers, but install it with SQL? My guess is it would come right up. But, it would give you some information. And, then you would have it work there, and you could then try to connect to the server. Of course, that would just be a trial to see how it worked. And, it would mean getting the key from support, since it would be a virgin computer for a new install.
The first thing I would try, though, would be to use an uninstall program like YourUninstaller! or Revo to make sure you are COMPLETELY uninstalling AC. I would always do that anyway. Maybe there are some .dll files or registry keys that are left behind which are confusing it. 9.2 should be out shortly.