Originally Posted by David Mc

Low battery is more than likely to be the cause of your problems. E70's originally came with a conventional lead acid battery, many of which did not last long as the car's computer modules can remain active for up to 20 minutes after switch off/locking. The situation becomes even worse if one or more of the car's modules continues to impose a parasitic drain on the battery (I believe the telephone module is the primary offender for this type of problem). BMW's initial response was to market a battery tender kit (basically a small charger that you had to connect to the car whenever it was parked up), but they have revised their initial response and now recommend AGM batteries for these cars. The conventional battery suffers permanent damage once the charge level dips below about 70%, whereas the AGM units are capable of far greater discharge levels.
A battery voltage of 11.4v with the engine running is extremely low - you should be seeing around 13.8 - 14.0 volts with the car running.
I would be checking the battery with a battery tester or a Digital Voltmeter with the engine off. If the car has been running for more than 20 minutes and the battery voltage is under 12.5v, it may be time to get out your shovel and bury the old battery.