Your thermostat should power on without a problem if it is battery operated, and even then, when you put batteries in it, it should still power up. Without knowing the exact model, the only other problem I can think of, the power to the thermostat is supplied by the furnace which is a common wire (usually blue) that is also hooked up to the C terminal on the thermostat. If there is a common wire hooked up, then you have to check if you have power to the furnace. If not, the problems could get more complicated. Hope this helps.
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Your thermostat should power on without a problem if it is battery operated, and even then, when you put batteries in it, it should still power up. Without knowing the exact model, the only other problem I can think of, the power to the thermostat is supplied by the furnace which is a common wire (usually blue) that is also hooked up to the C terminal on the thermostat. If there is a common wire hooked up, then you have to check if you have power to the furnace. If not, the problems could get more complicated. Hope this helps.