You should have the speedometer with the clear plastic case. Manually turn the input shaft and look closely at the gears in relation to the shafts that they are attached to. You are looking for slippage of the gears. When you locate the slippage, (or damaged gear) you will then know where to go next. Tedious work.

Do I have to take the needle and the face plate off?

It's common for a lot of 22-year-old cars!

__________________
Kent Christensen
Albuquerque
'07 GL320CDI, '10 CL550. '01 Porsche Boxster
Two BMW motorcycles

It will make things easier to work on. You don't have to fear scratching the face plate up if you have it removed. Bring the needle over the stop and let it come to a natural rest, and mark that location. Or, if your speedo is off by a few mph's, now is the time to fix it the poor mans way. Pop the needle off using steady pressure from underneath and from the opposite side from the needle. Be careful as it will go flying when it releases. Then you have the 2 screws. It's easier than it looks. When you go to re-assemble it, the needle pushes on easy. I had to re-glue the little black cap on my needle.

I will give it a try this weekend. One question, If the speedoometer cable is broken will the speedometer still work? Does the cable turn the odometer?

That's correct, No cable, no speedometer.