Hi Redvanman, This setup sounds very much like the unit I saw for sale in northern NSW Australia. If it is a true startomatic it should have a box, on top of the generator head, containing the starter relay, battery charging resistors and the wiring from the generator. It should also have a, second, control box containing relays. diodes and etc. It should look something like the photo attached and have a wiring diagram pasted in the back of the box.
What to do next depends on what you intend to do with it. If you wish to use it for primary power supply: strip it, rebuild it and it should last you for ten plus years. If you intend to use it as only a back up: get a service manual, change the oil and oil filter,
change or clean the air filter(depending on type), change the fuel filter. Having done all that give it a good run under load(an electric heater is ideal) and see how she runs.
With regards to the solenoids be careful, some run off 12volt or 24volt others run off the generator output, could be 240volt. Get a wiring diagram and an electricians amp/volt/resistance meter before doing anything that could potentially kill you. Better still, if in doubt, consult an electrician or post questions here.
Good luck and welcome.
Bob