central air wont kick in?
As mentioned above it could be low on freon, take a look at the copper lines if they are freezing that's good indicator (also could be a plugged coil too). You say it's intermittent, when it's working go outside to the condensing unit and see if the compressor is running for a while, when the fan inside is on. If it's running for a while and the air is cool chances are the freon is not low. If you're low on freon the compressor will cycle a lot. If you have a set of gauges check the freon, they sell a cheap, tire pressure gauge looking one at Walmart, I don't know how good they are.
Assuming that the freon is OK, and you seem to think it is, I would guess it's electrical. First make sure you have the wires on the correct terminals and that there are no loose connections. Try turning on the unit and jiggling the wires on the thermostat to see if there's a break. Thermostat wiring is usually thin solid wire that breaks easily if bent a few times or nicked when stripping. These breaks can happen inside the insulation and can't be seen. If you have some slack in the wire, pull it out and strip the wire back further and look for breaks. It may have been that the first thermostat was bad and that the wire broke from bending it when putting in the new one.
Don't do the following (there's live 220 Volt electric) unless you know what you are doing, you could cause damage to yourself or the unit:
You can jump the thermostat wiring in the condenser unit to see if it's working and if it's the wiring from the house to the unit.