I checked the continuity based on the document and everything checked out. I couldn't check pins 24 and 31 as they go to via holes on the PCB. I tried scraping some of the resist off above the via hole but was worried I'd inadvertently cut through a track.

I also checked adjacent pins for short circuits and didn't find any.

My next guess is the PROM failed, but I've worked on another product in the past which uses the same PROM and I don't recall any failing.