Outdoor fan runs but unit is quiet?
Intermittent buzzing sound and lights dimming?
Likely compressor isn't starting, check compressor run capacitor and continuity of windings*, incoming voltage.
*Compressor has three connections, u can ohm it out through the wires, check schematic on back of electrical access panel.
Resistance from S to C and R to C should be equal to resistance between S and R.
If all checks out you add a hart start capacitor and if it still doesn't start the compressor is shot.
If this is over your head or you're not comfortable it's best to call someone out.
You have to make sure the capacitor is totally discharged before touching it (it maybe charged and can kill you).
Multi-meter, meter that checks capacitance required.