If you have a digital or analog thermostat, you may be seeing a readout at the unit, but your air conditioner or furnace is still not turning on. The thermostat uses 24 volt power coming from the furnace or air conditioner. If there is no power to this wire, the thermostat will not be able to send a signal to the HVAC system to turn it on. You can check for power yourself with a few household tools.
Check the circuit breaker. Go to your breaker box and look for the breaker that powers the furnace or air conditioner. If these breakers are tripped, turn them back on and then attempt to turn on the furnace from the thermostat.
Check the power switch. There is power switch on the side of the HVAC unit. Make sure that it's in the "On" position, or else the thermostat will not turn it on. Attempt to turn on the unit with the thermostat.
Change the batteries in the thermostat. If everything seems to be wired properly, the batteries in the thermostat may be too weak to turn on the HVAC unit. Attempt to turn on the system after changing the batteries.
Test the power wire to the thermostat. Using a multitester, switch the tester to a range that will measure 24 volts AC. Clip the red lead to the power wire and the black lead to the negative wire. If there is no power to the thermostat then you will need to call a professional electrician to run a new wire from the HVAC unit to the thermostat.