I have a newly installed Bryant 2 1/2 ton compressor unit that was installed in August 2005. When I turned on the A/C the unit would not start. I checked the disconnect near the compressor and found it to be faulty and replaced it with a new one and there is still no start up. I pulled the panel to check the connections and found there was power to one side of the relay, but not the other. When I pushed in the contacts on the relay the compressor started, but shut off when I released the contacts. There is no signs of burned contacts or damage, but since the disconnect was trashed, could the relay also be bad or could it be the thermostat or both.
Although this unit is still under warranty, a $20.00 relay is cheaper than a $60.00 service call.

You need to check the coil of the relay to see if the thermostat, when set to "Cool" has 24 volts at the coil.

If no 24 volts, then the problem is with the thermostat, or the low voltage wiring to the compressor.

If you have 24 volts at the relay, then the coil is defective and the relay needs to be replaced.