Hi
sounds like a great excuse to learn about generators (you can't make it any
worse)
Basically a generator is a spinning coil (or coils)of wire which spin in a
magnetic field usually generated by another coil of wire.( I'm sure you knew
this).
But did you know the field coil is usually DC whilst the armature is
producing AC.
Most generator have a rectifier pack or voltage regulator connected to the
field and these often go faulty.
Another common fault (with long unused sets) is sticking brushes.
Yes they DO have brushes these bring the AC output off the armature and can
stick in their guides giving symptoms as you describe.
Find the brush gear and measure the voltage with the set running also check
the field voltage out of the regulator.
Oh of course check that the field windings are ok.

Just a few pointers to get you on your way

HTH good luck
CJ