This sounds like a problem with the Generic Electronic Module. If I recall correctly, all of these functions are controlled by the GEM. Also, the GEM contains the CTM or Central Timer Module, which controls the amount of delay on the wipers, the time-out delay on the dome light, door-ajar indicators, and the seat belt indicator time-out. I'd be willing to bet the "Warning Chime" isn't working either, which would surely conclude the problem is with the GEM. (try both the headlights warning chime, and the keys-in-ignition chime)
It's a black box on the driver's side of the compartment that houses the radio and A/C controls. Remove the "radio bezel" and check that each of the connectors are firmly in place on the GEM.
The Black Beast 5.0
Better to Have Horsepower and not Need it, than to Need it and not Have it!
2000 Ranger Sport - 5.0L V8 - 8.8 LS rear