I am embarrassed to say I found the fault. The problem was traced to a cause entirely external to anything manufactured by Nikon. It was good old User Error (otherwise known as stupidity on my part). But at least I'm prepared to admit it!
When I first got the flash it came with some alkaline cells already fitted. I ordered some NiMH cells and charged them, then removed the alkalines. I had just enough time to note that the spring contacts were all on the same (upper) side and note approvingly that this would reduce any tendency for contact to be lost if you were running and photographing - then the phone rang.
Later, I put the freshly charged batteries in and, without testing, went on holiday for a long weekend. I didn't have cause to use the flash, though I did take lots of UV, IR and LWIR images. It was when I got home I discovered the flash didn't work. I swapped back to the alkalines, to no effect, so I hit the various forums asking for help.
Today I sat down with the flash and a multimeter, planning to check the on-load battery voltage, the DC output from the inverter (thanks Shane) and possibly the voltage on the PC sync terminals. The battery voltage appeared to be 2.73V - clearly wrong! It was then that I realised the batteries should be inserted in the traditional down-up-down fashion: although Nikon were clever enough to put the springs at the top they weren't foresighted enough to arrange the holder so all the batteries pointed the same way.
Cut to the chase: Once I installed the batteries the right way round, the flash charged in 2 or 3 seconds and the Ready light came on. I swear it was laughing at me.
The bottom line is that I'm very glad I asked for lots of advice and WAITED before diving in to the device, trying to fix a fault that wasn't really there.
Thank you to everyone who has taken the time to consider this issue and made helpful suggestions. I am beginning to think I should give up on all this high-tech photography stuff and go back to making charcoal sketches (my talent for which is famously - possibly even legendarily - bad).