IIRC I had one of those apart many many (like 15) years ago. Perhaps Jrichker can confirm it, but there is a bulb for the display illumination. IIRC in this case the display did work but you had to hold the radio just right to see it. And in said case, the bulb was the issue.
If your display itself ate poop, I'd not wanna even bother. There's a ribbon and some other crap in there that would be a pain to trace.
I find the radios a PITA to reach anyhow - getting one with a remote is nice.
Good luck.