My car also starts and dies within a second of starting unless I hold the key in the starter cranking position for about six seconds or more to get me past that dead spot! It makes me think there is no fuel in the fuel distributor,maybe just a little residual in the lines by the injectors to give it that initial start and then it dies until more fuel can be pumped up from the fuel pumps.
In other words I think it is leaking back some how. I think there are check valves by the pumps and also a fuel acumulator back there by the pumps ,one of these may be the problem item.

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88 W124 3.0
96 R129 119eng
06 ML350
98 ML320 sold
02 CLK55 amg