Many years ago, I had a problem with a Paxman 4RPH, got a high exhaust temp alarm, seriously high and stopped it, Chief, Third and myself spent a week working on it trying to find the problem, 16 hours on 8 off. No Instrumentation on the engine, just a single exhaust gas thermometer after the Turbo.
Checked the timing perfect, overhauled the injectors, overhauled all the cylinder heads, stripped and cleaned the air cooler, stripped and cleaned the turbo and no joy. Eventually changed the fuel pump as it was the only thing we hadn't tried and Eureka, problem solved, the fuel pump shaft had sheered and it was trying to run on on 2 cylinders out of 4.
I was on another ship where one of the D/As shut down as soon as it reached 50% load, eventually figured out that somebody had swapped the governors over and not set it up correctly, at 50% load the governor output shaft was at its max. limit. Simply disconnecting the Governor arm from the splined output shaft and turning it slightly to match the other engines, cured that, lots of things can go wrong when somebody who doesn't know what they are doing works on a piece of machinery.
Remember that although most modern fuel systems are designed to be self priming, not all are, so it is worth slacking of the fuel injector pipes and cranking the engine over to see if fuel is coming out, that will also prove that the Safety Shut Down is not operating.
You say that you have a Low L.O. pressure alarm on starting, depends on the system on your engine, but if you don't have a "pre Lube" pump there will usually be a time delay before the L.O. Low pressure safety shut down operates after you press the start button, in order to give the engine time to pick up oil pressure, if this is set at too short a time then the fuel will be shut down before it can fire.
The Fuel stop solenoid is fail safe, that means there is a spring to shut the fuel off and the solenoid has to be energised to permit fuel to reach the engine, so if the coil has failed or is too weak to overcome the spring you will not have fuel.
Good luck with fixing it and a Happy New Year when you are done.
It is always better to ask a stupid question than to do a stupid thing.