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So far it sounds like a wiring error, that caused a fuse to blow.
If you can give me the brand and model number of the new thermostat, and a photo of the terminal strip inside the furnace or air handler where the thermostat wires end up... I can coach you on how to fix it. Use the paper clip icon at the right end of the tool bar above to attach the photo. Bend the wires out of the way so that I can read the terminal numbers.
The wires generally attach to the printed circuit card, that is located in the blower compartment.
I need to know if the unit that sits outside the house runs in both summer and the winter or not.
ooops... we can go from there.