Had exactly the same problem on my SE (1.
The car had been standing for a week and I'd been messing with the dials - when I came to crank it over, it fired and then died
I got the same flashing key light and thought I'd screwed the immobiliser by taking the dials out
Phoned the AA for a tow to the nearest dealership and he came out, cranked it over on his starter battery and it fired fine
Said it was "just flooded"
With a "low battery" fault too, sounds like the same problem
Maybe time for a new battery ?
It could be the alternator of course ... but batteries are cheaper to replace