I don't think it's an engine problem, unless its not running up to speed. If the engine is running at the proper speed I would guess the problem is on the back end. I assume it must have some kind of voltage regulator on it. I would first see if it had power, sometimes these are fused. The next thing I would do is excite the field with say a 9v battery. After that it's internals on the generator and might not be worth investigating any further. I am sure you can find documentation (manual) online somewhere. Find a tag on the back end (generator not the engine) and see if that company has a a website. Most manufacturers have manuals you can download for free.