I tried turning off Aero (but will try again). At this point I've tried everything including 3 installs of Win7, all sorts of new (and old) video drivers, power settings, and so on. Minimizing windows before sleeping is the only thing that has worked.
The reason I want to automate the windows minimization is that it is my wife's PC and she doesn't always remember to do this. If it were just me, it would not be a problem.
There must be some sort of scheduled task that I could set up to minimize windows whenever sleep or hibernate is invoked.