Well, after all the testing, it turns out to be a common 'stock' fault, albeit showing itself in an unusual guise.
The external power socket on these is notorious for its internal switch contacts sticking and causing the external power to be fed onto the internal batteries. But in this instance, the contacts were shorting out the internal batteries when the set was switched on. Im not sure how exactly, but 'exercising' the contacts (by plugging the external power lead in and waggling it about) has solved the problem. It remains to be decided whether or not i'll replace the socket.
So, here she is, complete with leatherette carry case and shoulder strap, and rubber duck antenna -