So, here's my take on a potential ticklish bit on the human factors side of things...
It seems like failure to /maintain/ the preheat button in a depressed state until /after/ the engine is started and, further, until /after/ oil pressure gets up to 10lbs, would be a common error for those unfamiliar with this family of generators -- and one that would prevent the generator from running. See page 9 of the operator's manual below:
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https://www.westerbeke.com/operator's manual/40457_rev2_7.6btd_operator_man.pdf
The schematics for the generator can be found on pages 41 and 42 in the service manual:
--https://www.westerbeke.com/technical%20manual/38673_5bcd_bcda_bcdb_technical_manual.pdf
Given the schematic, here's my take on the debug workflow...
Under normal operating conditions power to the fuel solenoid, which pushes the fuel rack into the run position, and power to the fuel lifter pump, are supplied via the circuit with the safety switches.
But, this can't happen until the unit unit is running with sufficient oil pressure to close the normally open oil pressure switch. In order to enable the unit to start, the "Preheat" button operates the preheat solenoid, which, via a circuit breaker, supplies the fuel pump. And the same starter solenoid which operates the starter motor supplies power to the fuel solenoid to push the rack into run position.
Since the engine is cranking, the start solenoid is doing its job. So, the side plate should be removed from the fuel pump to visualize the solenoid and fuel rack. If the rack is pushed into the run position, the problem is not there. If it is pushed, but not fully into the run position, the fuel solenoid may need inward adjustment, may not be getting enough voltage, or may be weak. That should be debugged by checking the voltage into the hold coil and back-tracking as needed, or adjusting the solenoid, as needed. If the solenoid is getting proper voltage, but is not operating the rack or in need of adjustment, the rack can be manually operated for testing. If the rack moves appropriately and the engine starts, the solenoid should be replaced.
If the solenoid moves the rack into position and then it falls back, that points to a failure in the "hold" coil circuit. It should be checked for 12V at the input to the oil pressure switch and debugged backward through the other normally-closed sensors to the source, as needed. If the oil pressure switch is getting 12V it should be /briefly/ bypassed. If this corrects the problem, oil pressure should be verified with a mechanical gauge and the oil switch replaced as needed. If the hold coil doesn't hold when given 12V, the fuel solenoid should be replaced.
While the preheat button is being pressed, fuel pump should be felt and listened to for activation. The output line can also be loosened to check for flow. If the pump is turning on but not supplying fuel, fuel supply to it should be (re-re-re-)checked starting with the valves and then filters. The supply line can also be opened and checked for flow with gravity or another pump. If there isn't a problem supplying fuel to the pump, and the pump isn't supplying a solid stream of fuel, it should be replaced.
If, when the preheat button is pressed, the fuel pump doesn't get voltage, the ground should be checked, and then the positive should be traced backward and checked at the circuit breaker, and then the preheat solenoid, and then the input to the solenoid, and then the coil to the solenoid and then the preheat button.
Cheers!
-Greg