my condensor won't shut off

If I switch the thermostat off the condensor doesn't stop and I can only make it stop by pulling the fuse block or switching the power switch off next to the air handler. I have removed the side of the condensor with all the power switched off and found no debret or webs and the contactor was open, when I switch all power on the contactor pulls in and the condensor starts but the tstat doesn't cut the low voltage to the contactor when it cycles?? If I remove one of the low voltage wires from the contactor, the contactor releases and the condensor shuts off. If I switch the tstat off the low voltage to the contactor is still on and the contactor stays pulled down? I have checked the 4 wires going to the tstat from the air handler and they are all hooked to the correct (Y G R W) without crossing, but someone has cut the lead outside the air handler and wire nutted the 4 wires together? When I remove the Y wire from the tstat the condensor doesn't stop but the air handle does stop. I'm thinking the problem is either my tstat or the wire leads have gone bad, but I don't have another tstat to try on it and need to ask if there is any way for me to test the thermostat to know if it is bad before buying one?

Your saying that when you disconnect the Y wire from the T-stat that the compressor doesn't shut off & just the condenser won't shut off but, the air handler end does?
This is a good one and hope it doesn't end up with a new control board.
Disconnecting Y wire eliminates the T-stat from the circuit but, compressor still runs. - T-stat = Ok?
Assuming no recent changes or work on the system. A short in the T-stat wires, (Y & R) would run the compressor non-stop.

If you can, disconnect Y&R from the T-stat & terminal board inside the air handler and check for a short.

I went to the house today and removed the tstat from the wall and trimmed the wires 1 inch shorter and rehooked to find the condensor now does shut off when the tstat cycles. I'm a bit affraid to leave the houst without switching the power off next to the airhandler in fear it may come on by itself and burn the compressor up. I'll keep testing it while I'm still working on the home to prepare it for sale. I had a sick feeling the wires may have been shorting and thought I should change the leads since they are only 8 feet long, and I may still do that since they've been spliced .I'm not really sure how to check the leads (Y&R) for a short since the ends are 8 feet apart?