If you put 12+ to the screw and 12- to the case and the starter didn't even flinch, then your brushes are most certainly burned up, and depending on your luck, the stator may have a short.
Starters are relatively straight forward to disassemble and service. Worst case, you can't put it back together and have to get another starter anyway. If you aren't interested in a project, just order a used one toss yours. Otherwise, take it apart and see what looks broken. Nobody here is going to know exactly why it isn't working. It's all guess work until you get it open and see what's what.