How could they test the generator if the engine didn't crank and run? Start by measuring the battery voltage. It must be 12.6 volts. If you find around 12.2 volts it is good but discharged. If it's closer to 11 volts it has a shorted cell and must be replaced. Charge the battery at a slow rate for an hour, then start the engine to continue. Measure the battery voltage again with the engine running. It must be between 13.75 and 14.75 volts. If it is low, diagnose the entire charging system. The generator is just one part of that.