First, make sure there is power to the controller's outlet. Use a test lamp or any other 110VAC device to determine if there is voltage at the outlet. If there isn’t power there, or if you have a controller that is hard wired, check the circuit breaker at the main breaker box.
Caution: High voltage testing on the transformers primary power side should only be done by a professional electrician or irrigation contractor.
If you have power at the outlet, the next thing to check is the transformer output. Use a voltmeter to check the voltage either on the two transformer wires or at the two AC screw terminals on the controller. The transformer should have an output in the range of 24VAC to 28VAC.
If the wall outlet has 110VAC and the transformer has no voltage output, you need to replace the transformer.
If this doesn’t restore the display, the controller will need to be replaced.