Sounds HPFPish :S. Do the diesels have HPFP? I do know they still have glow plugs just to pre-heat the combustion chamber and only had to wait about 2 seconds one morning to start our 330d. The temp was minus 19 Degrees C however! It shows a little coil symbol then cranks when ready. Normally, even when getting in and starting almost immediately, there is no delay!
Hope your 35d gets sorted!