2001 Blazer dies just after starting up.

my blazer starts immediately and the engine dies within 1-2 seconds. jumping it does not help.The fuel gauge has been faulty for years, but no check engine light. The battery indicator light remains on as the engine dies. There has been an unusual whirring sound from the engine on occasion recently and the battery has been dead on occasion without any lights or accessories on. Alternator? Fuel pump? Computer? Battery?
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