my experience w/ diesel comes from an old volvo d26. i'd guess you may have solved the starter problem w/ the new battery but to have it just die would be more in fuel delivery. once a diesel starts combustion is all compression. i'd start with the cheapest, inspect and clean injectors. then find the psi output specs for your fuel pump. again the volvo injector pump needed to put out a high psi to force the diesel through the injector so that the diesel vapor entering the cylinder is such that the compression, 24:1, would ignite it. best of luck
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