I have a 33gal craftsman air compressor serial #921-16472 and I have had to replace the off and on switch 3 times now because it is burning the points in them.

SOURCE: Sears Craftsman 3-Gallon, 1.5 HP Air Compressor Hums

YES IT MAY BE THE CAPACITOR . IT COULD ALSO BE THE WIREING IN THE MTR, THE PUNP ITSELF.

SOURCE: craftsman compressor motor/capacitor problem?

I had the same tripped breaker problem with a similar Sears model 919.195060 (25 gal) and luckily I had access to another, almost identical sears compressor to swap parts to diagnosis it. It turned out to be the run capacitor, but from what I was finding in my on-line research, it could have been a bad winding on the motor or the start capacitor just as easily. If your resistor is outside of the capacitor, just cut the wire right at the capacitor and add flag termnals Mine had 3 wires coming out of the capacitor (not the normal terminal cap style), and two of them were basically just tied together (same color). I didn't have an external resistor. I bought a GE 97F9614 run capacitor (40 mf, 370vac) and other than having to cut out a bit of the plastic on the mounting bracket and buying "flag" style 1/4" terinals from radioshack, it fit and worked perfectly. It seems if GE is the only one that has the right dimensions (1.75dia x 3.88 long, not including the terminals. That capacitor cost $27.50 with tax at a local electric motor shop. Sears doesn't even have any info on the motor parts, like capacitor - they want to sell you a new motor for almost as much as a new whole compressor. I ended up looking at parts forr the motor on a Devilbliss (that's what the 919 means on the model number, that it's made by Devilbliss), but it was not an easy way to go and really didn't help that much). The easier/normal way of matching capacitors is to measure the case dimensions carefully and match up the voltage and uf (or mf) specs,

SOURCE: craftsman compressor motor/capactitor problem?

It sounds like either the check valve or the switch that lets the air pressure off of the pressure switch is broke. After the compressor pumps to shut off pressure, when it shuts off, it should let a short burst of air from the switch. If it does this, that parts good. Give it a little time, then manually push that plunger on the switch.( you're trying to see if the check valve, which is a one way valve, is leaking air back into the cylinder) If air is release from that plunger, the check valve is leaking and will not let the compressor start, because air has leaked back into the cylinder.

SOURCE: Air compressor regulator installatlion

The arrow denotes direction of air flow; It should point towards the air hose connection(s)

SOURCE: My craftsman 3 gal. air compressor, 921.153101 won't compress air

I WOULD TRY DISCONNECTING THE PIPING FROM THE HEAD DOWN TO THE TANK AND SEE IF ITS BLOWING AIR. COULD THE COMPRESSOR BE RUNNING BACKWARDS - YOU WOULD HAVE HAD TO CHANGE THE WIRING IN THE MOTOR.
VALVES IN THE HEAD COULD ALSO BE BROKEN. YOU CAN REMOVE THE INTAKE AND IT SHOULD **** YOUR FINGERS AT THE OPENING. HOPE THIS HELPS.