He made it through the night, and I worked from home today so I could ring the vet's when they opened and later take him in.
It's difficult to tell what's actually wrong with yer pocket pets, but he's been prescribed Baytril, the small rodent antibiotic, by a nice vet who was very kind to both of us. She told me I was doing all the right things, which certainly made me feel better; I hope the Baytril does the same for Click.
I've given him a hot-water bottle, bought him some baby food (at julietk's suggestion) and made him some apple purée. (God help me if I ever get a cat, which are actively demanding.) All I can do now is leave him to it, and try to resist poking him every five minutes to see if he's still alive.