I've seen the RainDial do some crazy things. Mostly on controllers manufactured in the mid to late 90's. The manufacturing date is in the battery compartment. I've never seen one do what you're describing but it wouldn't surprise me. I haven't see the circuit board where the wiring's connected go bad. It's always inside the faceplate. If it's too much trouble to install a new controller you can simply swap out the faceplate with a new one. You can't buy just the faceplate. You need to buy the whole thing and pop it out.
www.sprinklerwarehouse.com/v/vspfiles/search/search2.asp?Extensive_Search2=N&keywords=raindial
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Just make sure the problem is indeed the controller before you buy a new one. This one is a tricky question. I'm not convinced it's the controller yet.
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Do you have a master valve? If not unplug the controller when there's multiple valves running and see if everything shuts off. Even if they do, crossed wiring can cause multiple valves to water at the same time. Like I said, make sure it's the timer before buying a new one.
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Good luck!