Odometer quit working but speedometer works fine

There is a plastic gear in the speedometer that eventually breaks on mechanical speedometers called an odometer drive gear. This will involve removing the speedometer from the instrument cluster in the dash.

If the speedometer is still working, but the odometer does not, most likely the cable is broken (separate drives for odometer and speedometer within a single cable) or the dash unit needs replacing...

SPEEDOMETER TROUBLESHOOTING

Can be loose speedo wiring connectors under instrument panel or its issue with speed sensor on transmission.

I suggest you to go through help links mentioned below with appropriate solutions to confirm the problem :------

How to trouble shoot speedometer?

http://schematicsdiagram.blogspot.com/2011/06/speedometer-not-working.html

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1996 fiat bravo speedometer not working?

http://technoanswers.blogspot.com/2012/01/1996-fiat-bravo-speedometer-not-working.html
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Speedometer works but odometer not working?

http://technoanswers.blogspot.in/2012/01/speedometer-works-but-odometer-not.html

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Speedometer runs backward?

http://technoanswers.blogspot.com/2012/01/speedometer-runs-backward.html

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Warning lights on and speedometer died?

http://howtobyme.blogspot.com/2011/08/warning-lights-on-and-speedometer-died.ht

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Speedometer not working on 1993 Ford F350?

http://repairhelpcenter.blogspot.in/2012/02/speedometer-not-working-on-1993-ford.html

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ABS & Brake lights warning indicator steady on dash and speedometer not working for Dodge Ram?

http://howtobyme.blogspot.com/2011/11/abs-brake-lights-warning-indicator.html

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Vehicles Cluster panel Not reading Miles?

http://schematicsdiagram.blogspot.com/2011/12/vehicles-cluster-panel-not-reading.html

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Odometer works properly but speedometer works intermittently?

http://technoanswers.blogspot.com/2012/01/odometer-works-properly-but-speedometer.html

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These will help.

Thanks.

could be the VSS - vehicle speed sensor .
Speedometer and Odometer
The Vehicle Speed Sensor (VSS) is a gear driven permanent magnet generator. The vehicle transaxle houses the VSS. The VSS generates a sine wave output with a frequency proportional to the vehicle speed.
The Powertrain Control Module (PCM) converts the CKT 389 signal to an output that switches to ground at a frequency of 4000 pulses per mile. The CKT 389 signal drives the speedometer and the odometer. Various other vehicle components use the CKT 389 signal. Refer to Engine Controls.

It is most likely the speed sensor in the transmission.

You need to replace the speedometer gear that drives the sensor.

The odometer part itself is bad.

Could be a ciggerette lighter fuse, usually cause this when it blows.

Suggest you visit this website... http://www.hyperocity.com/volvo240/volvoodometer.htm
Odometer is turned by a mechanical gear wheel, which is the likely culprit.