I have a similar problem (I think?)... my car starts and cuts out after 1 second. Been researching like mad online and reading up about all the various problems it could be.
First thing I did was try a different key. No luck. Then I called the RAC and his tablet showed "17978 Engine control unit blocked - permanent". So he recommended I try replacing the 409 relay switch. Still no luck. After many attempts at starting, my battery started to die. Charged the battery - but not convinced it's holding enough charge. It's an old charger and not very advanced.
I read about people experiencing similar problems and it's accompanied by the immobiliser symbol (car + key icon) flashing. Mine doesn't flash but tried the trick anyway of leaving the ignition on for 10 mins before starting. And it appeared to work! It started up and I took it for a spin. Came home, shut engine off, started it up again to check. All good, I thought. 5 mins later, tried again and it won't start!! 10 min trick doesn't work either. So it may not have been that that 'fixed' it. I also wiggled some of the battery fuses around so I thought maybe that did something? I'll try again tonight. Also read that the ECU can fail if it gets wet? I have been having damp problems in my car that I'm trying to fix. Not sure if it's related. Just can't tell where the problem lies - if it's ECU, battery, immobiliser, key transponder etc.
Don't really know where to turn now. Oh yeah, and my partner is due with our baby in 3 days