I agree it is likely starving from fuel but it could be the relay. You can try swapping the starter relay with the fuel relay (they are the same). After the swap, if
the starter turns the engine, you know it's good. If not, you know it's bad.
For fuel, you must be sure the filters are
clean and the check valve at the very top of the tank is not jammed up with crap. This check valve is at the top of the tank and is threaded to a 90 degree barbed fitting. Stuff growing in the bottom of your tank (from water) can get sucked up into this check valve and jam fuel before it gets a chance to fully flow into the fuel pump. There is also a small metal CO2 sized pre filter connected to the fuel pump. It may be clogged and you can't tell if it is because it is metal. This CO2 sized filter is sold at your local NAPA Auto Parts Store - part number 3046 (about $8).
In a 2013, you unlikely to have a failed fuel solenoid. In my case, as per below, I needed one. My generator is a 2006. Once I replaced the solenoid ($353), all was good. Solenoids do wear out over time. And when they fail, they fail closed thus starving the F Panda of fuel. And they can close (i.e. fail) after they get hot so you might see your generator run for a while then simply die.
2006 Fischer Panda 4200 installed in my 330 Express. 985 hours. My generator has been otherwise reliable but recently I can't get it to start. The starter turns the engine over and over but no start. About a month ago, I had gunk in my tank which plugged up the pump's pre-filter & fuel pump...
www.greatgrady.com
Hope this helps... Good luck!