Hi Mark,
I'm not familiar with the 300SEC, but your symptoms are indicative of a flooded engine. Try depressing the throttle about halfway down when it doesn't start and see if it doesn't allow the engine to clear itself more quickly. Your fuel pump noise is probably due to the fuel having lost pressure and taking a little time to pump it back. You might possibly benefit from one of the snake oil fuel injector cleaners... possibly not, also.

Good luck with it,
Richard Wooldridge
'82 300D/4.3L V6
Etc...