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Hi I'm Brian and I'm here to help!
Since your thermostat had no batteries then you have a 24 volt common wire on the thermostat C terminal. If you put good batteries in the thermostat and made sure they were in properly, your thermostat should have powered up. If it didn't then I'm sorry to say your thermostat is DOA. If the thermostat powered up but the system wouldn't run then you may have a deeper problem. If you have volt meter, check for 24 volts ac between terminals R and C on the thermostat. If you have 24 volts ac, that's good news! Try removing the wire on G and touch it to R. That should turn on the indoor blower. If you don't have 24 volts ac between R and C or the G to R bypass doesn't bring on your fan, you likely have either a blown low voltage fuse or blown low voltage transformer in the air handler or furnace (whichever you have).
Let me know what you have with the tests above and we can trouble shoot further if you like. I will need the make and model number of the indoor unit to help you trouble shoot further.