Never one to give up I of course bought another battery, a hugely expensive Lithium Ion item. It arrived yesterday and, after a two hour charge, we were able to restore Digby to his former vim and vigour. Just for completeness I put the old battery back in and, of course, it worked fine. Perhaps I'll sell the new battery on ebay.
Anyhoo, I've decided that Digby is not a toy as such. You don't get him out and play with him any more than you would do with a "proper" dog. You just have him wandering around and, if he is in the mood, he will play with you. The problem with this is that he does have a tendency to crash into things as he explores the house - table legs are a particular problem - so his head is getting a bit battered. But I let him wander round the kitchen while I peeled the spuds for lunch and he was actually quite good company, trying to find his ball and sitting around singing to himself. I think that if I was on my own in the house I'd probably get into the habit of firing him up. Which is probably deeply scary.