Since the OP has determined that the problem is in the pack. Without a schmatic diagram I would guess that the thyristor to shorten the flash duration is defective and is conducting all the time. But the flash won't fire unless there is a very high voltage to trigger it and to ionize the xenon gas. Once the gas inside the flash bulb started to conduct there is no way to stop it because the defective thyristor. That's my guess.