Your fuel solenoid is powered by the battery, but before we move from here, you'll need to make sure your battery is fully charged. If your battery is in good shape, then we'll proceed.
When you turn the key to the start position, the switch should be routing 12 volts to that solenoid, and a lot of times you can hear the little "click" sound that is associated with the solenoid engaging. If you are not getting 12 volts there when you have the key in the start position, the first thing I would check is your battery cables where they connect to the battery. A poor connection there could cause that. If that looks good, then check your ground wire going to the engine block or the frame of the generator to make sure it is secure and making a good connection. You know your solenoid is good since it functions when you add a 12 volt source to it, so if your cables and grounds look good, then the next thing you'd look for is any bent, broken squashed, cut, or otherwise damaged wiring between the switch and the solenoid and also between the battery and the switch. Then there is your switch...it is also possible that your switch is bad and the reason 12 volts dc is not being found at the end of the fuel solenoid wire is due to that fact. Look into those few things mentioned above and let me know what you find. I am always interested in the outcome of things I have given advice on, and am glad to help you with anything else you have questions about.
I might be able to get a wiring schematic for it, but I'll need the model number on the frame of your generator. There may also be a revision, or serial number to go with it that I'll need also. Look for that model and let me know what you've got.
Ok, I found a diagram of the wiring schematic, but it is in pdf format which is not compatible with JA's system here and I don't have a printer handy to print and then scan it in with. I will be able to add that wiring diagram first thing in the morning if that suits you ok. I'll get it on here asap.
have you any luck on the diagram?
Yes, I got it right here....the scans labeled #1 and #2 will line up side by side, number 1 on the left and number 2 on the right and the wiring lines up that way....the third scan is just another view and it has the definitions for each label. Wire number 14 is tied to your fuel solenoid and passes through a resistor(R1) before going to a start/stop relay(SSR). On scan #3, you can follow wire 14 and after it passes through that resistor(R1), the wire changes to #4 and splits to go two directions...one end to one of the brushes going to the rotor via the slip rings, and the other going to an electronic voltage regulator. I don't know that my input here will help you run this problem down any better, but I figured if all this looks like greek to you, it may give you a clue. Please let me know what you find as I am always interested in the outcome of anything I give advice on.