On my 90 325I, the fuse gets corroded. I have to clean out the connection every now and again in the fuse box under the hood.
The gears in the speedometer are stripped. If the odometer is working then you have input.
Probably the cheap black plastic odometer gears(2) if you have set in center. If you have odometer on the left and trip odometer on the right then it is two sets...four gears. Usually when one breaks the other is not far behind in the two set type. There are several online suppliers who can provide parts for the repair.
If the speedometer doesn't work either, then the cable broke or came loose. Otherwise, the gears in the odometer broke.
If you open the odometer, there are two small plastic gears. One is connected to the speedometer, the other to the odometer. The speedometer gear drives the odometer gear. In all likelihood, one of these gears is missing a few teeth. I have the same problem with my Ramcharger, same year.
There is a pair of gears driven off the Speedo cable. One or both of the gears have most likely broken. I have a set on the way. Sorry, haven't changed them yet, so I can't give you details on how-to yet.
If the instrument cluster is just mechanical then you will need to pull it out and check that the gears and rod that connect to the odometer are working and still connected and if they are then you will need to have the cluster overhauled by a certified speedometer shop........
Replace the speedo head assembly. It is a sealed unit, with no servicable parts. If the speedometer is working, then the cable and the speedo drive gears are working. The failure must be inside of the speedo head assembly itself.
The gears inside the odometer broke due to heat and age. You can buy the gears and replace them yourself. Or you can take your car to a place were they work on odometers.
Lower gears in the rear end means that the wheels will turn more than expected for a given gear and engine rpm, so the odometer will read higher than it should.
The odometer's gears are wearing out. For more information go to http://cabby-info.com/gauges.htm#odometer .
If the odometer is not working but the speedometer is still indicating speed, the most likely fault is a set of small plastic gears inside the speedometer instrument itself. I have seen these gears available for sale at various BMW parts specialists. Removing the dash cluster for access to the speedometer is not difficult in a 1987 E30 car. With the cluster on the bench, you can repair the speedometer gears or replace the whole thing. Used speedometers are plentiful at on-line auction sites such as eBay.
Gears is what transmission is for. No gears. No transmission!