My central a/c (Rheem) quit working. Opened the unit and the contactor was fried-completely burned. Replaced the contactor. Can physically push in on the center connections of the contactor and the A/C unit comes on and runs fine (as long as I'm holding it in). Will not turn on by itself. Digital thermostat will kick on the furnace fan, but cannot get the A/c to kick on. Yes it is over 80 in the house and the thermostat is set on 68. It is turned to cool. I've tried clicking to off and back to cool several times. All digital displays look fine.

What next? Which wires from the back of the thermostat would I connecct to get the A/C to turn on to verify that the thermostat was bad? Choices are: green, yellow, white and red.

The red and yellow,, if wired according to rule of thumb should start your a/c but sounds like you might have some shorted wires,, start at the a/c unit looking for chewed or uninsulated wires that could be grounded or touching,,

Tried the yellow and red at the thermostat nothing. Trying to trouble shoot my way through.

Furnace and fan work from thermostat just not the A/c
Replaced the batteries in the thermostat just to be on the safe side-no difference.

Opened furnace circuit board panel. Didn't see any fuses at all.

Breakers are not blown in main circuit box are not blown.

Fuses on outside box by a/c are not blown.

No power in the thermostat lines at the a/c unit.

There was when I first reattached the wire to the new part. Got a spark when I pushed it on. I'm not seeing anything that looks out of place.

With your volt meter,, check see if there is 24 volts at the furnace end of stat wires that are going to your a/c unit,, if you do,, then check for 24 volts at end of stat wires in a/c the two smaller wires that tie on or plug into your contacter,, if you have power in furnace but not at a/c,, would be easier to replace the wire from furnace to a/c

It seems to me that is not the thermostat even though it could possibly be it. Sense the thermostat is calling for heat lets assume that is good. Your problems is that the contactor is not pushing in to allow the 240v to go to the unit and it only works when you do it by hand. Well, what it is, is that your contactor coil is not receiving 24volts to energize it. What you need to do is to check from the inside unit at the board your red and yellow wires that are going outside. If this wires are alive(24v) then they might go to another board outside if you have a heat pump, and if from that board to the contactor there is no power in the wires hooked to the contactor coil then is the board(it could be a relay in the condensing unit board). You need to check for loose or ground wires. It could be that. If you have no power in the yellow wire going outside in the board that is located in your inside unit (evaparator unit) then is your thermostat for sure.

I have the same scenario at my house. The red wire is energized at the furnace, but the yellow isn't. (obviously no power at the contacter either). I thought it had to be thermostat, so I put a new one in. Same results: Blower fan in furnace comes on, and I can physically press in contacter to engage capaciter, and, condenser. What did you figure out for yours? I am about to run a whole new thermostat wire.
Thanks

On the side of my furnace/blower is a pump to get rid of condensation. It was clogged with filth and the float rose so high that it activated a kill switch to the whole unit. Cleaned out the pump, and got my thermostat signal back to the outside condenser. $0. Hope this helps.