My 1990 bmw 525i trip odometer light stays on, and the speedometer stops.

Odometer
The instrument panel cluster (IPC) displays a season odometer and a trip odometer. Momentarily press the trip/reset switch in order to toggle between the season odometer and the trip odometer. Press the trip/reset switch for greater than 2 seconds, while the trip odometer is displayed, in order to reset the trip odometer. The odometer is calculated and stored electronically in the body control module (BCM). The BCM uses the vehicle speed information from the engine control module (ECM) to calculate the odometer. The odometer displays 'error' if an internal IPC memory failure is detected. The IPC stores a backup copy of the odometer value incase the IPC stops receiving a valid odometer value from the BCM. The odometer will display 'error' if an internal IPC memory failure is detected.

Your best bet , take it to a qualified repair shop .

oddly enough, check the wheel speed sensors. there are 4. the fronts are the same the backs are the same but the fronts are not the same as the back.

Unless you have a totally stripped-down Eldorado, your speedometer is most likely ELECTRONIC (probably even has a digital readout).
Check your Trip Computer. Has it stopped reading fuel economy, distance to empty, etc.?
Is your odometer also not adding miles as you drive?
If affirmative to all of the above, replace your SPEED SENSOR, and you'll be all set :)

If you have someone check the engine computer for trouble codes, you'll probably find a code for the speed sensor in the transmission.

power distribution box problem ,take ti out look underneath and no doubt the links corroded out ,well for the dipped light anyway the stop light is no doubt the switch faulty so replace the stop light switch .

ABS pump went bad.

problem with service schedule that depend on milleage

yes the transmission speed sensor has most likely failed, to confirm this have a trouble code test run

check your speedo cable it runs from your transmission to the back of your gauge cluster. its probleby broken or disconnected

1990 bmw 525i when charge light stays on when car is shut off