It was the bike controller, I guessed it would be.
I took the old controller out, and removed the end of the box; a small amount of water trickled out. Not good. I've left it to dry out, maybe it will recover.
Meanwhile, I installed a new bike controller, bought from electric-hybrid-bikes.com some months ago against just this contingency. I had to rewire the throttle so that the wires matched, and I had to over-ride the lock connector so that it thought that the bike is permanently unlocked. Then I lifted up the front wheel, applied a bit of throttle, and it worked! I've tried to make things a bit more waterproof, by putting the controller and the wiring into a zipped pouch that looks like it should ward off the worst of the water. I think the problem happens when I pressure-wash the bike. That pressure-washer is really high pressure.
So I've ordered two more bike controllers (from China), because electric-hybrid-bikes.com were out of stock for 24 volt controllers. I don't need it in a hurry, that's the whole point of having a spare lying around.
I also ordered a controller tester. They're only £9, and it sounds like just the sort of thing I'd like to have.
So now bike.2 is operational again. Bike.1 is the other Haro DX; it works, but I need more batteries to use it in the field, and I'm still trying to extract my order from Hobbyking. But bike.3 is also operational, that's the Everest folder that I converted a few months ago using the extra motor that I got from AlienOcean and a controller from electric-hybrid-bikes.com. All these bikes are 24 volts, so I have interchangable batteries.
My experience with Hobbyking batteries has given me an idea. I could run two of my old 24v 10AH packs in parallel, and I can do that simply by making up a lead that makes that happen, cost near-zero. If my idea works, then that would make bike.1 operational even before Hobbyking sort themselves out.
Speaking of which ... I did a LiveChat with them last night, the operator was named as Daisy. Daisy (not that I believe these names, I think they generate them automatically) said that everything that Mary told me was wrong, and that I wasn't going to get my order until:
1) I send back the wrong order they sent me (I've done that, and have proof of receipt)
2) Hobbyking's UK warehouse acknowledge that they've received the order (which happened a week ago, and they haven't acknowledged yet)
3) They get new stock of the batteries that I want (date unknown).
Daisy offered to send them from Hong Kong, but I said no, because A) it would take a week or more, and B) I'll have to pay import duty, and VAT, and a fee for someone to do that.
I'm thinking this is all going to take a few weeks. It's just as well that I'm not in a hurry for this ... but don't tell Hobbyking that!