Compressor comes on but fan is turning too slow to blow any air out.

Sounds to me like the A/C clutch is no good and out of adjustment.You should goto your nerrest junkyard and get a used assembly take the clutch off then you learn how it comes off and install it on yours the save the pump for later use if needed. The clutch should only have a .010 air gap after install between th inner elctro magnet and the clutch plate it's self.

sounds like a blockage in the refrigerant circuit, the compressor is shutting down, protecting itself. possibly the compressor is overheating, possibly it's overcharged.

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could be a bad run capacitor or, the motor is bad. have the capacitor checked that would be the cheapest thing only about five bucks

you have a slow leak in your refrigerant and need to find the leak. you will have to get an AC repairman to come to your house and check it for leaks and fix the problem.

Most a/c's have a 5 minute delay before the compressor turns on and they will do the same when changing from cooling or heating to cooling.

sounds like the compressor is turning off cause of high pressure. check the coil that the exhaust hose connects to, if dirty clean it. if the fan is not blowing enough air threw the coil the unit will build up high side pressure and cut out, but will turn back on when pressure drops. if that dont help, maybe the fan motor is bad or needs taken apart and oiled.

if the fan outside is turning on and inside fan is blowing too, then you have a compressor problem. could be a capacitor gone bad (or needing a hard start kit) to the entire compressor failure

If the fan blows cold air the compressor is already on.

Fuses are a protection device and I guess that this is for the condenser section and compressor. If they blow right now when it is turned on would indicate that there is a short in the wiring or motor or compressor. If it trys to start and the outside fan starts and the compressor just humms and blows fuse, you have a locked compressor. Might check run capacitor or install a hard start kit and see if it will brake it loose, if not bad compressor

Isthis a window unit? It sounds like it. There could be a problem with your fan switch or the fan motor itself? Multi-speed motors can lose one speed at a time. It really sounds like the fan motor is bad. If the compressor starts in the cool mode, and the fan doesn't, the fan motor could be locked up. See, if you can spin the motor by hand? If you can, then something is bad within the motor. Now, if the motor has a capacitor, check for a loose or burned wire. Good luck.