The compressor has an internal short. Toss it to the recycle bin. Find a BJ's warehouse club near you and get free air.
Unfortunately, no BJ's are found here on the west coast. But you must live in a stingy neighborhood where they charge you for everything. Don't tire shops give you free air? Anyway, I think I'll switch to the cordless Dewalt inflator.
It may be just that the compressor needs lubrication or the motor bearing is gunky. A few drops of gasoline or a spirit perhaps. Lithium "LM" grease is non conductive and good for motors that get hot. That or connect it directly the battery and see what bit goes on fire kill or cure.
I would bypass the plug on the compressor wire by peeling back some wire before the plug on the wire. I would stagger the peeled portions of each wire so they are not next to each other. Next I would splice in and tape up some heavy duty wire with alligator clips on the ends (or make my own up out of an old lamp cord ..etc). In one of the wires I would add an inline fuse 15 amp (or whatever size fuse is normal for your cigarrette lighter socket in your car. Next, I would raise the hood on my car and connect the alligator clips up directly to the battery. If it runs and doesn't cut off or blow the inline fuse then you have just eliminated the compressor or its components as the problem. The problem will likely then be in your car wiring, fuse block, or cig socket in your car. More than likely the cig socket.