On Carrier the start capacators are both in the same can (Dual cap).
Try it in FAN mode. if the blower works Good. or bad, depending on your POV.
If it starts to run when the compressor kicks in but, then a few seconds later it stops and ***IF*** the green light flashes like five times (or groups of five) you have a major problem. POSSIBLY loss of coolant, This is a service call.
On teh Carrier Air V there is a spot just off the compressor where two lines dip down in a "U" shape.. Just like a plumbing trap.. This is, in fact, a vibration trap designed to keep the vibration of the compressor from causing problems down stream with cracked joints and such.
Problem is the idiots let the two pipes touch, and they wear each other out and HISS goes all your coolant.. Also it's a hard spot to fix. Replacement may be in order... IF you do replace it I think Coleman, and I know Advent Air, make a drop on upper unit for Carrier ducted non-heat pump models. THis is less expensive than a entire unit.. Save the blower and the cover.. May need 'em some day (I saved the blower, fan, motor that runs them, cover and start capacitor assembly)