My lg window ac units compressor is staying on even when display is off. The only way to shut it off is to unplug it. I disconnected the display board from the pcb board and the compressor still ran Im thinking about replacecing the pcb board but I was wondering if the capacitor is only a start or a run capacitor and can that be causing the problem. Thanks in advance for any help.

Why would you think the capacitor has anything to do with it? If the compressor would not start and the meter indicated that the capacitor was shorted or open then you would replace the capacitor. What you have is a stuck relay. Sometimes you can tap them with a screwdriver handle and get the contacts to unstick, but you will need to solder one on the circuit board or find a way to wire in a new thermostat if it's one of those electronic units. It is possible to do this. If you get it unstuck wire in a relay running on the circuit board where the circuit board is only energizing the coil on a relay and you have fixed it. You can buy a small relay at any HVAC store.

I wasn't sure what all the capacitor did I always thought they were just for starting the compressor basically a jump start. But any way I also did research and the fact that the contact sticking makes sense but Im not sure where the contact is.Its a printed circuit board with relays Im asumeing a relay is also considered a contact. If it helps you help me the model is lwhd1500er. There is a relay that says ry compressor I think that may be shot also to test this relay I should be able to do a continuity test across the terminals right, if it reads it's a closed contact if it doesn't its open and open is what it should be. I have basic knowledge of some of this stuff but appreciate all help on the matter if it was only a $100 unit I would have just tossed it but I paid $420 about 2 years ago so its better tio try and fix it plus it's a learning experience. Thanks again in advance..

You can do a continuity test on the relay. One set of terminals is the coil and will have a high resistance. The other sets are contacts. There is usually a tiny drawing on the top of the relay showing the contacts. One is common in the middle and the others are normally closed and normally open. If the normally open one is welded closed you can tell with the meter. The capacitor helps with starting and running torque. There are two kinds: run and start. The run has low microfarads and is wired from start to run and the start is connected by a relay where run feeds it and the other side of contacts goes to the start terminal. See: https://dl.dropbox.com/u/8010163/How%20to%20use%20Test%20Equipment%20Service%20Manu al.pdf
https://dl.dropbox.com/u/8010163/Compressor_Data_Manual.pdf
These will explain things. You can find replacement relays at Radio Shack, but it's best to use the output to drive only a coil on a relay and wire one common to compressor as it already has been done and break the other leg through the new extra relay. It's easy to figure out.