From my photographic experience, this charging sound means that the flash is trying to charge, but when it does not get ready it probably means it cannot detect the capacitors to be charged to a sufficient level to trigger the flash procedure.
Which model is the flash in question?
Measuring the capacitor voltage whilst charging would be an idea. Caution: can get dangerous when something goes south...
(I remember a colleague with whom i photographed some public festivities some years ago, where we did visitors that were partying in the rain- I protected my flash with a plastic bag, he went some time without... Later that evening, he was photographing in a big disco, and being near the dancefloor, his flash finally went "BOOM" - no parts flying around, but EVERYONE in that room (fittting around nearly 1000 people...) turned heads...
Another idea might be the holder/contacs of the flash bulb itself, or some circuitry that checks it- Flashbulbs can be damaged also.
(In one of my older flashes (Metz 54MZ-4i) the flashbulb was soldered to make safe contact, so that might not apply.)