If the speedometer works but the odometer does not, the odometer has failed.
They both work off of the same signal. If the speedometer works but the odometer doesn't, the odometer has failed.
Bulb is probably defective. Replace it.
Your relay sensor is likely faulty
Most likely the cluster is failing.
There may be a broken gear inside the odometer.
If the heat in your 1990 Chrysler New Yorker is not working, it could be due to a faulty thermostat, a clogged heater core, or a malfunctioning blower motor. You may need to have these components checked and repaired or replaced by a mechanic to restore the heat function in your car.
If all do not work - check fuse in power distribution block under hood
Yes.
tripometer doesn't work either.
possibly a broken internal gear in the speedometer head
The wiper motor on a 1992 Chrysler LeBaron won't work if the motor has seized up or the fuse has blown. The switch inside the cabin or the wiring can also come loose and cause this problem.
If both the speedometer and odometer are not working I would suspect the VSS (Vehicle Speed Sensor) is at fault. If the speedometer doesn't work and the odometer does, I would suspect the instrument cluster is at fault.