Seems like I have read posts where CS2 will not work on Mt. Lion as it has a different file formatting or some such thing.
To further Curt's comment.
Photoshop CS2 was PowerPC code, no?
Mac Mini's are Intel-based sysetms. The Apple emulator program "Rosetta" was required to run PowerPC code.
Rosetta has long since been abandoned by Apple, so you're going to need to buy new Adobe software or subscribe to the Creative Cloud to continue to use Photoshop.