Sometimes solenoids buzz. Could be the controller. Could be the wiring.
None of your valves are working. There's probably ONE cause for that.
One of the three RainDials I looked at made the solenoids pulsate. It also did the same wild flashing when I reset it.
I'm still suggesting you replace the controller.
www.sprinklerwarehouse.com/v/vspfiles/search/search.asp?Extensive_Search2=N&keywords=raindial
Do you have a master valve? Maybe that hidden valve is the master valve. Is it working?
***Do you have water at the valves?*** Please confirm this. Open a bleeder screw.