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!
2006 BMW E60 520d SE 6MT
2009 BMW E90-LCI 330d SE 6MT
Current: 2012 F30 328i Luxury 8AT
2015 Audi A6 Avant Ultra, Black Edition (sorry!)