Transformer is typically wired directly to a dedicated circuit breaker in the power panel. It doesnt go through a relay as it controls the power to the relays. If you arent getting power to the transformer, the controller won't work as well as any buttons on the panel. Trace as to why the power to transformer is not hot. Likely a tripped breaker or loose wire. Normally white wire to neutral buss and black goes to hot side of breaker.
Sounds like your controller is wired with a gfi protected plug in outlet so likely they just connected to the hot side of one relay to tap into constant power? Take some pics of the panel open and feeder to the gfi so we get a better und rstanding of how it is installed. If you arent confortable working with electrcity, an electician will likely get you up,and running pretty quickly. Good news is restoring power to,the transformer will likley fix your problem and is much cheaper than replacing the controller board!
Do you have a factory surge supressor installed? If so, there may be other causes / wiring will likley be different than described above.
