First, let me say that this is a cheap, old Shimano derailer that's getting junked and upgraded anyway, but I would still like to understand what's wrong.

So, here's the problem: The derailer is not angling up when I upshift. It's staying in the same downward position throughout the whole range of speeds. As such, the jockey wheel is about 6 mm from the largest sprocket and about 46 mm from the smallest. It's making downshifting very difficult in the upper speeds. I'm thinking a spring has failed in the derailer, and as this is one of Shimano's cheapest-made models, there is no way to adjust or access these springs.

Am I right in my thinking, and would there be anything I could do about it if I weren't already planning total replacement?

Are you able to post a photo?

A missing spring seems a reasonable guess. These springs usually hook into mounts inside the derailleur. Look closely to see whether you can find two spring-sized mounting holes that are empty.

Actually a missing spring would mean that the der body would tend to pivot forward as the only remaining chain tensioning spring, the cage one, will try to wrap as much chain as possible. this means that the cage/upper pulley will only be limited in it's travel by contacting the cassette's underside teeth. The opposite of what was above mentioned.

Much more common then a somehow lost spring (the Op didn't take things apart and forget to install the spring, did he?) is a stiff upper pivot. As this pivot gets tighter from corrosion (or grit) the springs (both cage and upper pivot) can't provide enough tension to either rock the body in either direction.

Some pivots can be dissembled, cleaned, lubed and reassembled. Just don't forget to install that upper spring. Andy

I've only had the cage apart so I could remove the derailer from the chain, but I didn't disassemble it any further, at least not knowingly. I don't really see a way to take it apart, as everything looks to be riveted together. I was able to take a casual look at another identical bike today, and it doesn't seem to move much up and down, but I wasn't able to remove the chain to see how the springs behave without any outside tension. This one, however, extends to its most obtuse limit when the chain is removed. That's what leads me to consider a possible failed or missing spring.

Ah, more data. With the chain removed and when pulling the der rearward is there spring tension? Is this movement free and easy? Andy.

With the chain removed, the der goes straight down and won't pull rearward. If I pull forward on it, there is spring tension, and it snaps right back down to the limit.