The easy stuff always first. Had a very similar problem with a Volvo, got a new battery and solved the problem. When the fuel pump goes bad you will hear it is my experience.

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1979 Black on Black, 300CD (sold), 1990 Black 300SE, Silver 1989 Volvo 780, 1988 300CE (vanished by the hands of a girlfriend), 1992 300CE (Rescue).