I had this issue as well and managed to solve it. Roman's third link actually points to right solution. The problem is in fact with cards that have more then one GPU on them. Mine is, for example, ATI Radeon HD 5970 which has 2 GPU-s. Some old games, including JA2, have issues with those cards and in order to play them you need to disable second GPU. Disabling AI in Catalyst setting does the trick.
However, the problem is how to disable it since the option doesn't exist in Catalyst drivers anymore.
I use a freeware program that manages profiles for that purpose.