Thanks, ʇɐb ɹəuəllıʍ, the Windows Installer Cleanup Utility allowed me to complete the uninstall, which was at least 50% of the problem. After that I had to sweat blood granting permissions or creating entries for at least 50 registry keys. But now that that is all behind me, Adobe Reader is up and running again.
By the way, I do have administrator rights.
When I mentioned "sweating blood" I was referring to "seizing ownership" of the subkeys, as detailed here: http://social.answers.microsoft.com/Forums/en-US/w7repair/thread/71cdd66a-75ce-4e79-bace-8 9637e0dacae
Sometimes I had to go up a level or two before I could influence the subkeys. And sometimes I had to add a new key. In a few instances I had to name the key "command" or "win32" or whatever Adobe was looking for. In other instances I added a "new key" and then the subkeys that belong to the key in question appeared out of nowhere. In cases like these, I deleted my "new key" and proceeded to adjust the permissions on the subkeys. Since I was always going back to the same header keys, after a while I started adjusting the permissions on all the subkeys of the headers I was using: for example. if the header was HKEY_LOCAL_MACHINE\SOFTWARE\Adobe, I would adjust the permissions on all the subkeys. After each registry adjustment, I tried to install the program. I found that I was constantly being sent back to the same registry "headers", so I started to adjust the permissions on all the subkeys of these headers. I believe that this shortened the process.