So I popped it in again (after soldering the original power supply wires back in). It also took me quite a bit of remote debugging to get the display and my MediaCenter software properly communicating, but after about an hour that was all fixed. But lo and behold: the exact same segments don't light up!
Odd indeed. I need to debug, but with the display in the case, it's harder to debug it. Guess it'll have to wait until I have lots of time.