Could it be a knackered ignition switch?? My red BB4 has a broken ignition switch and so turning it to the 'on' position doesn't actually turn anything on other than anything on the 'accessory' position - turning it further to the 'start' position turns the starter over but as the main ignition isn't on the car won't start. It's had a separate switch and relay wired in for the ignition as a result which works fine but would probably cause an insurance company to have a jobby fit*.
It also had a drokked main relay (both the ignition and fuel pump circuit) - that caused the car to not start either, and it did produce the symptoms of an immobiliser being on (no fuel or spark).
I soldered the main relay and it's on my to-do list to replace the ignition switch, but the car never fails to start now.
*FWIW if there has been an immobiliser fitted to the car and you remove it, your insurer may void the theft part of your insurance policy - Direct Line wanted me to take my BB4 to a garage and get a letter from them confirming that I had a Thatcham cat 1 device fitted. I didn't want to pay a garage for this so they just advised that they couldn't provide theft cover as a result, due to their policy on underwriting imports

The mad thing is that the UKDM version probably wasn't immobiliser equipped, and I'm sure they'd provide the theft element of cover on a UKDM 4g no questions asked...