I have spent the last week dealing with this exact issue. I can attest that what Roy says is correct. My injector 1 MOSFET was dead. I know absolutely nothing about electronics - all I did was remove the dme and took it to an auto electrician who said that injector 1 MOSFET tested differently to the others but couldn't tell me if it was busted or not.
My experience is that as soon as you say BMW and ECU or computer people generally switch off as very few dal with these. I did find some knowledgable people but they ignored what I said re symptoms and wanted to do all this other stuff. Not saying it doesn't apply but I bought the Mosfets from a computer store and a tv repair place fitted it.
This absolutely works. I suggest you replace all mosfets if you get the 30BA or 30BB code. In my case when it went it took out the cylinder 1 coil as well which I replaced first as I wasn't sure if that was causing the issue.
All in all a relatively easy fix but difficult to pinpoint as there are so many things that could be an issue. I felt compiled to reply to this as it really helped me and hope it help others.
Thank you Roy - you are a legend!!!