I have done the measurement on the 240 I drive. You guys might want to do this first if your speedometer do not work. It might just be bad connections from the sensor rather than a broken instrument board. Steps to dismantle the instrument cluster may be referred from this link (http://www.hyperocity.com/volvo240/volvoodometer.htm).
See below illustration. After the instrument cluster got removed, find for the 3 wires with L-shape connector as shown in the picture. Note that wire color codes have been changed in later models, however it still serve the same purpose.
Then, using an analog multimeter (can use any type of multimeter, even an oscilloscope), connect the -/COM lead to the BLACK wire terminal, and the + lead to the BLUE wire. Note that the RED wire supply voltage for the board, because we are not connecting the board, leave it. BLUE wire is transmitting signals from the speedo sensor.
I set my multimeter to read AC voltage as follows;
Start the car, and get moving, slowly. You should be able to see the multimeter readings increasing with the speed of your car. This indicates that the signals from the speedo sensor at the axle was fine. If with this condition, still the speedometer do not work, I suspect the instrument board itself must be checked.
Good Luck :)