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Is the display LCD? It looks like the actual segments are glowing rather than being rear-illuminated, so that makes it LED or VFD.
The only chance you have is if you can track down the problem to a poor contact. There may be a ribbon cable (or flex foil) which connects the display to the circuit board, or the display itself may be in a socket of some kind. Careful!
I'll bet that the display segments are multiplexed, if they are it's not going to be a cable or connector problem as the same segment would be missing from all 4 digits. It would have to be dry joint to that single segment or a faulty segment