Oh great and wise HDI Gurus...

[Niall]

Starter motors don't really get lazy, if it's slow to crank your battery could be a bit weak and that can stop it from starting - the ecu won't fire the injectors unless it sees adequate voltage.

I can't speak for all ECUs but most have a working voltage of 8-18v so the first thing to give up working with a flat battery will be the starter won't crank or won't crank fast enough. Most ECUs will not inject though until they see a certain RPM from the engine, in the case of most I've come across this is about 400rpm. Once it sees that, it will switch over to its idle running.
HDi ecu may be completely different but thats my experience of all the ecus I've dealt with in the past.