Three possible Suspects
1: As discussed above Start cap.. But wait, that costs money (not much)
2: Motor (blower if it does not start and blow air) Sized,, (Big money)
3: (no money) Nesting bird or insect blocking condenser fan from turning. (or the blower for that matter).
Suggestion: "Pop the top" (remove the outer cover) and give it a good visual inspection take flashlight, if you see nothing make sure blower/fan motor shaft turns freely (Turn fan with hand) this is all power off stuff.
Post results, but if the thing turns.. I'd go with option 1 (Start Cap)
NOTE: While you are up there, and have the cover off.. Might as well remove the inner covers as well and clean the Condenser and Evaporator coils (as needed) and anything else needing cleaning for that mattter.