I purchased the exact same model (NF-2 light tower) off CL a couple years ago but I didn't keep it long. I only bought it for the enclosure to house my MEP-002a in, so I sold the engine on CL for what I paid for the unit. The engine in mine was a replacement engine and ran like a top. One thing I did have to do was replace the condenser on top of the box where the plug wires go in, it was faulty and had been bypassed by the previous owner. Condenser was a bit hard to find as I recall. So when you attempt to start yours is it turning over a bit slow or fast? It should turn really fast as the generator has slip rings and it is used as the starter and it does an excellent job spinning up that engine. I can't tell from the picture but you are starting it with 24 VDC as in (2) 12V batteries in series, correct?
I would also open up the electrical box that sits on top of the gen head and take a look inside. There are just a small handful of components such as wire wound resistors and capacitors that you should verify are still good (look for signs of overheating, etc.). Mine did have a flakey problem where I had to position one of the side toggles on that box in a particular position or it would not start...Can't remember exactly but I seem to recall it would start using the remote panel switch but not the inside switch on electronics box or something like that.
Also, there are quite a few very knowledgeable people over at SmokeStak.com that are quite familiar with the Onan CCK engine. You may want to start a post over there as well if you want to leverage those resources in addition to those here on SS. Your probably not going to get a lot of people over here all that familiar with this unit.
edit: I do have some close up photo's of the engine/genset for comparison purposes if you need to verify something (verify position of linkages, parts, etc.). Let me know and I will post if needed.