Thrmostat does not show a read out... does this mean that it is not longer working and I need to replace it in order for the air condtioner to work?

Did you replace the battries? Does the furnace have power?

I bought a new thermostat recently and hooked it up. I know the wiring is correct because I checked the wires all the way back to the furnace. The furnace is working, but the air conditioner (http://www.houstonairconditioners.net/air_conditioning_replacements.html) will not turn on even though the wiring should be correct. I checked the filter, and that is clean. The only other option suggested to me was that maybe the thermostat wasn't compatible with my furnace/air conditioner. How do I know I'm getting the correct thermostat? I checked the manuals, and they don't say anything about a specific thermostat needed. The new thermostat I have didn't have any specifications that I noticed

Did you put a jumper from rh to rc?