Unfortunately, there a number of possibilities presented in your description. Obviously, electricity is not the problem since the light is on. The clicking could be as simple as a relay or solenoid that is not working. There is probably one in the system that actually turns the electric motor driving the compressor on and off. The relay or solenoid would respond to inputs form the system pressure as well as thermostat requirements. In the worst case, the refrigerant (a gaseous chemical) may have leaked out, but the symptom for this would be the compressor running without ever shutting off. Bottom line is; I don't believe there's much you can do about it other than calling a serviceman... Best of luck!