Hi Mike. Mine stopped at 154,000 miles. Common problem. A plastic gear breaks in the odometer. There are actually two gears known to fail, although I only replaced the more common one. These are user serviceable.

Not a cable - it is incremented by electronic pulses. When you get it fixed, you can see this if you look closely. It steps. The computer knows the actual mileage, by the way. With a 1996 you would need a reader to get it.

I found the FCP Groton had the best price, because if you order other stuff you need (you must need SOMETHING for your car), the postage turns out to be very low. Using other sources such as the odometer gear wizard (sarcasm) they kill you on postage.

The procedure takes 2-3 hours and patience. Maybe someone who has done this recently can point you in the right direction. I used the method where you carefully pry the left side of the dash up. You need some small torx tools as I recall. My dash lights had all been replaced, but if yours haven't you might do those while you are in there.

If you have a trip computer, remember to look for the electrical harness. The site I used didn't mention it. If you have a turbo, there is a vacuum hose to disconnect. There is one site that has most excellent pictures on this procedure.

I googled "Volvo 850 odometer repair" and here is one site it returned:
http://www.volvo-forums.com/t4449-odometer-repair-instructions.htm

Good luck. Don

Former 1995 854T Owner. Miss it badly. Current owner of toy-like '05 V70 2.5T