Benzmac, all three lights (battery, brakes and emergency brake) are on. Does that rule out a brushes problem?
As a further description, as it was cold this morning I poured hot water on the injectors before starting the car and, out of curiosity, poured some over the alt. After the engine started, the lights went out and stayed out for a few minutes. Then all 3 came back on.
As I need to fix this ASAP (it's really annoying not to be able to blow warm air in the car at 0 F) I'm bringing the car in this morning.
Thanks all for your help, I'll let you know it turns out to be.