The cause of your speedometer failure is more than likely those dead batteries. You should replace them before trying anything else.

The procedure is fairly simple. First you disconnect the car's battery. Then extend the steering column out as far as it will go. This should allow the room necessary to remove the instrument cluster by unscrewing the three screws located at its top edge. Next carefully pry the cluster away from the dash. The whole thing comes out as a unit. The next step is to unplug the incoming cables. There should be two or three on each side. Be careful to note the position of the smaller wires coming in because on mine (1984 733i) it appears that they can be plugged into the wrong receptacles.

The instrument cluster should be clear now. On the back of the cluster are several screws holding the thing together. I can't remember exactly how many screws there are but I believe it's about eight to 10. After removing the screws the assembly will come apart. The different components are simply plugged into each other and come apart with a gentle tug. On one of those boards you will see the two AA Ni Cad batteries to be replaced. They are held on by solder joints at the battery ends to the contact plates and again from the contact plates to the circuit board. The way I did mine was to use a de-soldering iron to remove the solder from the joints on the circuit board. This can also be accomplished with a standard soldering iron and some copper braid (all available at Radio Shack along with the new batteries). The old batteries are probably glued to the board as mine were. An Exacto knife or utility blade will make short work of this (don't cut yourself!).

You must be sure to charge the new batteries prior to installation. This is a very important step and must not be skipped because putting uncharged batteries into the system may overtax the components and cause a failure. The way I put mine in was the simplest way I could think of. I purchased two single AA battery holders and ran their leads through the holes in the bottom of each. They lined up with the holes in the circuit board almost perfectly. The holders themselves secured nicely to the board with some gasket maker (any kind of decent adhesive should work well here). You must install the carriers as tightly together as possible to minimize the clearance problems you will have when it all goes back together. Make sure to allow time for the adhesive to set (like while the batteries are charging). When the adhesive sets and the new solder joints are done you are ready to install the new batteries. I felt it would be prudent to use a piece of tape to hold them in place.

When all is done and reinstalled the indicator lights should function normally again and will clear with the resetting procedure. This method I figure will greatly simplify the process the next time the batteries die, which I suppose will be in two to four years. I hope you find these instructions useful.

Good luck,
Kamron