Honeywell RTH7600 does not responsd
If you swapped out the thermostats with the power on, you could have shorted out the transformer. Best case is a blown fuse, worst case is a blown transformer. Do you have a C wire at the thermostat? If so, test AC voltage (VAC) between R and C.  You should get between 24 and 30 volts.

The furnace breaker should be in the main panel, or there will be a servicemen switch near the furnace. If a fuse is blown, it will be on the control board inside the furnace.