First check to see if there are fresh batteries in your thermostat. Most thermostats are powered by a transformer in the air handler and use batteries to back the memory but some thermostats function solely on battery power. Look for a seem down the side of the thermostat or a thumb tab that can be depressed to release the two halves. When separating the front from the base you need to support the base half of the thermostat with one hand to avoid pulling the anchors out of the wall. Some thermostats have a battery compartment that slides out once the catch is released.If your afraid you’re going to break it then you’ll probably need to cal a service technician from here. If you were able to get it open then read on. Some thermostats contain a small fuse. also if there were bad batteries make sure they didn’t leak. If you suspect the batteries leaked you can try new ones but be warned that battery acid can get on the circuit board and cause the system to do unpredictable things. Its usually best to have the thermostat replaced when this happens and make sure they get replaced yearly.
If there were no batteries or you replaced them and the screen is still blank, then you have more serious problems, the thermostat could be bad or there is no low voltage coming to the thermostat. There may be a safety switch shutting off the unit, its best to let a professional discover the cause when it comes to low voltage control wiring.Last but not least check you breaker for the furnace or air handler or heat.