Connecting 2 different power supplies in series
Assuming the power supply outputs are DC, you can do that provided the two supplies are isolated - that is, there is no common ground between the two.

If you're talking about the typical wall-wart, chances are quite high that it's a flyback topology switching supply, which is isolated. That's probably also the case with the ATX supply, but I'm not positive. The ATX supply's ground wires are not isolated, so you should use it as the "lower" supply - with its ground being the actual ground for the target device. Connect the wall wart's negative output to the ATX supply's 12V output and the wall wart's positive output will be 12 volts higher relative to the ATX supply's ground.

The current capacity would be limited to the lower of the two capacities of the source supplies.