166 Cutting out

Hi

My 2001 2.0 Ts has an annoying habit of cutting out while at traffic lights etc. After about 20 mins it starts ok. The AA have told me it's the immobiliser, there's no power to the injector or fuel getting through.
Alfa specialist plugged it into their diagnostic tool which says 'low battey voltage, ' Incompatible key' and key not saved'. The last 2 entries are probably cos 1 of the blippers I have doesnt work.
The only other symptom the car has is that the drivers side passenger door lock doesnt work and if you open it, the lights flash but the alarm doesnt sound.
If anyone has any ideas, I'd be really grateful, it's a lovely car.
I've done some searching and found some hits for a similar problem on a 156. Seems like the possible cause may be the crank/rpm sensor.
The symptoms seem to tie up i.e. engine restarts when sensor cools down. Anybody have any more info or seen this on a 166?
Should this error show up on the Alfa diagnostic the dealers use?

Thanks