If its a wall wart it could float anywhere off load
We've got similar post office scales at work.
Try disconnecting the ribbon cable to the display, and reconnecting it, not saying it'll work for you, but saved ours.
Silly questions...
Is there a manual available for it?
Is there a reset sequence - I used to have a Salter scale that had similar problems, used to reset it until it finally gave up the ghost and I replaced it with a cheap digital kitchen one.
Years ago, I fixed a similar set of scales by simply removing and then refitting the socketed ICs. Could be worth a shot, just in case any of the pin connections have gone high impedance.