Probably the battery (not) charging light itself.
The light carries the exciter current to the alternator for it to work correctly - if the bulb fails i.e. does not light with the ignition on and the engine not running - then the alternator will get no exitation current - the battery will not be charged by the alternator and quickly run flat.
This from Wikipedia...
The wire supplying the field current is often referred to as the "exciter" wire. The drawback of this arrangement is that if the warning light fails or the "exciter" wire is disconnected, no excitation current reaches the alternator field windings and so the alternator, due to low residual magnetism in the rotor will not generate any power. However, some alternators will self-excite when the engine is revved to a certain speed. The driver may check for a faulty exciter-circuit by ensuring that the warning light is glowing with the engine stopped.
Good luck...
Peccavi, February 2010