The best test to try is flashing the field. Take off the back cover (before doing this take a peak at the windings just to make sure nothing is obviously toasty) then take the leads off the brushes and secure them out of the way, put a set of temporary leads on. The positive brush is usually the one closest to the bearing. Start the engine and then hook your leads to a battery. The generator should come up to close to full voltage. If it does there is a problem in your excitation circuit. Could be a capacitor or a voltage regulator or another problem (hard to say off the top of my head with no print). If it doesn't make voltage while flashing the field then you have a problem with your rotor or your windings. You can check the rotor with an ohm meter slip ring to slip ring.
This applies to brush type, if you have diodes in your rotor one of those could of failed. However they can't be tested in circuit and have to be de-soldered which is kind of a pain so it's best to try and eliminate other stuff first.
If you need any more help feel free to PM me I'm a generator technician by trade.
Good luck and hope that helps