I have old Rheem furnace which air conditioner also connects to. After I replace thermostat, now the furnace and AC will not start. I believe most likely the fuse is fried, but where is the fuse? Attached are pictures of my furnace.

I don't see any pictures attached. Depending on the age of the furnace there could be a low voltage fuse on the circuit board,it will be a 3amp auto blade fuse. If the furnace is older it may not have a fuse and you may have blown the transformer. I would double check your thermostat wiring before replacing anything.