First things first, try tightening up all screws in the unit - this can sometimes fix this sort of thing.
Secondly, if the above doesn't help, super-carefully bend the battery contacts up a little bit using a tiny flat-head screwdriver. I always do this with old virtual pets anyway, because age and use (or, for new-old-stock units, being stored for decades with batteries inside) tends to push the contacts downward, and it can prevent proper contact from being made with the batteries.
If neither of those work, it most likely means that the polariser (part of the display) has deteriorated due to being stored in poor conditions by the previous owner.