Back in the 1980s and 1990s, if you were doing serious hardware development, you bought HP Logic Analyzers and Tek Oscilloscopes. The HP analyzers were more polished and more reliable; likewise for the Tek scopes.
To debug electronics from that era, I'd suggest finding a HP165x, HP166x, or HP167x series analyzer with a big set of cables, flying lead adapters, and test clips. The earlier HP163x series are OK, but limited in channels and the cables are clunky. The woven ribbon cables from the later series are nicer to work with. The HP16500 series are big loud boat anchors and always seemed to be breaking.
You really want to find an original set of flying lead adapters so that you won't have signal integrity problems. I'm not sure if anyone offers cheap replacements, but the originals were special micro coax with integrated compensation.
Screen burn is common with old HP analyzers if they've been left powered on for months at a time. I don't think I've seen any that are unusable, but it's something to check for and maybe negotiate a lower price.