Those cars have problems with connections at the back of the instrument pack, even when they haven't been stored outside with no convertible top.
First thing to check is whether or not the trip computer is ticking off distance traveled, and whether or not the cruise is working. All three speed signals come from a transducer mounted on the differential on a '90 model year XJS. If you have none of these functions, the transducer is the item to test. PM me if you need good used one, they are horribly expensive new.