If you have trouble uninstalling a product I would try Microsofts Installer cleanup utility.
you can remove a program's Windows Installer configuration information. You may want to remove the Windows Installer configuration information for your program if you experience installation (Setup) problems. For example, you may have to remove a program's Windows Installer configuration information if you have installation problems when you try to add (or remove) a component of your program that was not included when you first installed your program.
Bear in mind it doesn't remove the application itself, after running it, you then have to remove the application with a 3rd party uninstaller.
I would wait and see if any other members have any better solutions. This application would be the last option for me.
Once or twice I've had a similar issue, not with AdAware, though. I've found that reinstalling the application, rebooting (as prompted, or even if not prompted) allows it to then be uninstalled.
If AdAware 6 is still installed you can try to find (in programs > AdAware 6'folder) the file install.log.
If install.log can't be found you can't uninstall it normally. If you have yet the AdAware 6 installer you can try the expeditious Tarq57'suggestion - however the new install.log will not have the same installation info. But works out your problem. If you haven't the AdAware 6 installer you need to do a manual uninstallation.
Windows Installer Clean Up don't works here - AdAware is installed with Wise Installer that don't use Windows Installer.