My 91 Volvo 940 has been dying lately and won't restart. If you jump it, it restarts, but then sputters and stalls within about a minute. Before it stalls, the speedometer bounces up to about 20 mph even as your sitting still. The mechanic replaced the alternator and I took it back in and he sez it still tests like it needs a new alternator.
If the alternator bench tests okay, but doesn't work on the car, suspect the small wire connected to the alternator. This wire should be getting 12 volts when the car is switched on. It gets its power from the ignition switch through the battery light in the dash. Does the battery light come on when you turn the ignition on with the engine off? If that bulb is burnt out the alternator will not charge.
Also check to make sure that you are getting 12 volts to the small terminal or connector on the alternator with the ignition in the on position. The alternator is internally regulated so there is not much else that can be wrong if the alternator bench tests as good.
You have a data link connector on your Volvo. It works by flashing an LED a number of times. It would be worth checking the engine fuel and ignition systems with it to hand. www.volvoclub.org.uk/faq/EngineOBDCodes.html has a good tutorial for this vehicle. Be wary of spending good money on this vehicle though, cost of parts and availability of parts can be a bit hairy.