Kids while playing in the backyard were banging against the outside compressor unit and I found later that the display on the thermostat is now blank. So I can not switch on heating or air conditioning. Since my house has two units one for upstairs and one for downstairs, I tested by swapping the two thermostat units. The thermostat unit itself is OK as swapping makes the thermostat with blank screen to light up and the working thermostat does not work when put on the defective location.

There appears to me some fuse issue either at the furnace in the attic or at the outdoor compressor, but unable to trace the fuse or the problem. Please help.

You are missing 24 volt power to the thermostat. You will probably need a meter to track down the problem. Actually there is no simple cure for this except to test the components (transformer and wiring) to find the problem. You can check to see if the circuit breaker needs to be reset for the inside unit and that is right in your electric panel. The outside unit will have a disconnect which might be fused. That can be checked also.