Low coolant will not affect Fan or compressor short cycling. What is odd is you state you had the Tstat disconnected and the unit came on. THAT points to a upper control board, but that would be extremely rare. You have what is known as the 5 button CCC tstat system. A compressor staying ON, when it should cycle OFF, points to a sticking compressor relay on that upper board. If that is the case you must replace the upper board. Have you had any work done on the AC system? Replace the other AC? Capacitors also will NOT cause this type problem. Doug