This starting problem is common with E46 diesels and mine behaved exactly like yours. The first thing to check is the relay that switches the low pressure fuel pump. When you turn on the ignition, you should hear a satisfying 'clonk' from a relay behind the glovebox, followed by a slight thrum from the fuel pump. The relays will probably be as shown in this illustration, which is for my 2004 E46 320d Touring: bmwfans.info/parts/catalog/E46/Touring/Europe/320d.../ . In my case, the BMW dealer wanted a day's work to diagnose the problem - I bought the relevant relay (which is a light green colour, BMW Part No 6136-8 373 700) for £6 and put it in myself, then no problems at all, so a whole load of cash saved. Reading threads on BMW forums, there are many people who have been skinned alive by dealers changing pumps, filters etc, before finding out that it was the £6 relay all along. Locating the correct relay was for me a matter of substituting each one in turn until the fuel pump ran - I'm sorry that I can't remember which one is which. To access the relays you have to remove the glovebox assembly, which is not as bad as it sounds - quite easy in fact.
If you can hear the fuel pump running, then it's something else, but the relay is the most likely cause of your problem.
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