I have the same problem.
I disassembled the controller and realized, that the pcb is burnt in two areas:
1. in top-right corner (large resistor and 3 capacitors around it)
2. below the leds, under the zener-diode
I replaced the capacitors and switched on the 24VAC. The resistor became hot in 1 minute and 24VAC started flashing.
At that moment I realized, the the zener-diode became also hot, which is a surprise for me, because zener-diodes have typically 10mA current....
Desoldering the zener-diode and giving the 24VAC, the controller worked as before (bad), but one of the electrolit condenser became warm, so I unplugged it.
As there was no sign on the zener-diode I could not replace it and to tell the truth I think this problem is not the fault of the zener-diode, it only shows the fault.
Because the controller is full with SMD parts and there is no documentation I do not really think, that I will spend my time with debugging. It is cheaper to buy another type of irrigation timer...