electrageek,
waross's suggestions are good. For me, I usually skip to my variation of his step two: "disconnect the AVR and run the set with a twelve volt automotive battery for excitation. Shut down and reconnect the AVR."
For my variation, I have found that for most small generators (<1250kW or so) that a 6V lantern battery works just as well, it is easier to carry, and it does not require jumper leads that are so long as necessary to reach from the engine batteries to the generator voltage regulator that is sometimes some distance away from the batteries since it is located in the generator junction box or sometimes in the switchboard.
I would also add that if at this point the generator is not producing some voltage greater than the unexcited residual voltage then this is usually an indication that some other problem exists.
If this doesn't work and the generator engine is battery started by 12V or 24V batteries (versus air start), I usually repeat step two using the engine batteries.
I have never tried waross's "step three", mostly because I wasn't smart enough to think of it before I read his post. Nice suggestion waross, I'll add that to my 'bag of tricks.'
My usual "step three" is what waross does not recommend. That being said, I would not recommend it myself unless the recommendation was given to someone that had experience and someone who was very careful and if I did, it would be as a "last resort".
The last resort is to flash the field while the generator is running and the voltage regulator is connected. This flashing is only momentary, literally just a "touch" of one or two seconds of the battery to the field terminals. The danger that I have considered in doing this is not that the voltage regulator would be damaged but that the battery would be damaged and/or explode once the voltage regulator activated and applies a large (ie. up to 50VDC) voltage to the small (ie. 6VDC) battery. I have done this successfully many times. However, this is a method that is not recommended to persons who are not very experienced and that it is a procedure that is inherently is risky..."do not try this at home".