hi...this is absolutely odds on to be caused by a very common, simple and always overlooked or dismissed reason. happens so often with these mpi and caught me out a few times in the early days too. I am made more positive by the mention you made around the momentary kick as you let go the key.
So here it is...it's the battery. I will just about bet my salary on it. Briefly, here is why.
These mpi require an absolutely perfect health battery and of the required rating too. If anything less than this...what happens is that despite the engine cranking apparently fine enough...in this situation and with a less than perfect battery, the act of cranking will take all of the power available from the battery and not have enough juice to also power the vital other systems like sensory items, ignition system or even if the cranking rpm is less than a certain speed, the injection system too. it just won't even try....that is, until the brief moment you let go of the key. for a split second, there then becomes power available (because the starter has relinquished its demand) to bring the system to life...but alas, by then its all too late and will only give a slight kick or cough. sometimes you can catch it into life on the throttle...but only if you are lucky. trust me...try another known good battery or boost it. she will almost certainly fire up.
good luck
but i have to because of your description.