Despite what you might think, it might pay to start with the battery anyway. What voltage is it showing when the car is switched off, then when the car is running - is it charging at the right voltage?
I read a good comment elsewhere that the clock is BMW's canary - it can be the first sign of a faulty battery before the car dies.
Do you charge the battery with a conditioner/charger, or just rely on the alternator to keep it charged?
With a faulty battery there may be enough voltage to start the car, but the drain while starting kills the clock and accessories.
