I spent some time in the garage this evening. I've now freed and lubricated all the old cables. They are all completely shot, of course, but I don't want to buy a lot of new parts until I have a better idea whether this bike will run for me. The old cables will allow me to test things without spending the money for new ones.
I also pulled the rear wheel off, and opened it up. The brakes were similar to the front: nearly new, with lots of life left in the shoes. Lots of rust on the drum as well, but that will rub off soon enough. The back has a fairly prominent groove in the drum, though, so after I detemine whether the bike will run, it will need resurfacing.
I put the rear wheel back together, and reinstalled it with a new chain. (I didn't mind this purchase: if the CB160 turns out to be a dud, I can use the new chain on my CT200.)
I also figured out why someone would park this bike with so few miles on it: they didn't! The speedometer cable was twisted in half, so the miles shown on the odometer are not accurate. I have no idea what the real mileage may be. I expect to find that the speedometer is frozen, so I'll be lubricating the movement before I try hooking it up with a new cable.
I also tried spinning the engine over with the starter, using jumper cables from a fresh battery. No action at all, so I'll be pulling the starter off to see what the problem is.
Sorry I didn't take my camera out to the garage tonight!