Some RD's have a fuse and some don't. If there was a fuse you'd see it. I only have one thing for you to try. Take the battery out. Unplug for 10 minutes. If you still have no display after replacing the battery the controller is shot.
I suppose it's possible the battery terminal is broke off and the transformer is bad. You said the controller has power though. Maybe the transformer and the battery are dead. Press the battery against your tongue. That's what I do.
Ok I lied, one more thing. Make sure the faceplate is plugged in securly to the circuit board.
Here's some replacement controllers.
www.sprinklerwarehouse.com/Irritrol-Rain-Dial-Remote-Ready-Series-Controller-Timer-s/94.htm