BIG TIME PROBLEM with fuel system

Hello,
I have a diesel,*model KAD 42 A-P*I cannot figure out what the fuel problem is. The engine will start*when we are trolling and run excellent for hours, but when I put the boat in Idle it will shut down immediately. I then try to crack the injectors I have fuel to them, It takes about a half hour of cranking the starter to get it running again. Once its running I will put it in gear and trottle up but it does not respond. Only after a miute or so will it start to rev up and go. So far I have changed all fuel lines ,transfer pump,fuel filters*checked the fuel pickup and return fittings. When the motor shuts down I have fuel to the fuel filter. I am going crazy trying to figure this problem. (could it be the fuel shut off solonoide, if so how do I check to see if its working)*If you have any Ideas please feel free to shout them out..
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Thank you

The rack in the injector pump is sticking. It would explain why the throttle will not respond. You may want to pull the injector pump and have it checked out.

if pump checks out try disconnting shut off solonoide and test engine.

I may be wrong, but in the marine application, the fuel shutoff requires power to kill. Disconnecting it will do no good.

Pull the injectors. If you have a tip blown off it would act like this.

By haveing to prime the injectors to get it started again, sugest that there may be a leak that it is sucking air . go over all line connections on fuel system ???? and having to fill the filters confirms that there is a sucking leak or a restriction in the tank that is pulling up into the pick-up appond aceleration then will fall back to be picked up again and again

Do you use Racor pre-filter(s)? If so, they are notorious for air leaks. Air in fuel lines will give you the symptoms (cranking but not starting, not responding to throttle, surging of engine, etc). Sounds like you need to take them out and rebuild them (replace o-rings to re-seal the housings).