2003 BMW 530d auto immobilised, with zero electrical life?

A few days after using ( rarely ) the spare key several times on one day, the car alarmed falsely for a couple of days. To stop this occurring during the night, the car was left unlocked ( in a secure driveway ) overnight.
The following morn., - all dead, - no sign of power; other than ( ONLY ) the front nearside sidelight remaining on for a few hours. Suspecting a dead battery, jump leads applied as per BMW procedure; without sucess. Immobiliser suspected. No lights or accessories were " left on " when car was left unlocked overnight, and the is a mere 3 months old, and fine.
Both master "remote control" keys tried in various permutations. Still - everything dead .
'Have a few theories, yet still unclear which to go for first.
Any ideas that may target and solve the situation?