I had a battery light, too, and an intermittently failing power steering. Some days later, a burning smell in the passenger cabin and the battery light permanently on. Luckily, this happend 2 km from my place. I drove home for diagnostics: the alternator had permanently failed. Also, no power steering once the battery voltage went below exactly 12.0 V. This meant charging the battery at home. As it was an old battery, driving without the alternator with power steering was only possible for 5 km, beyond that range, the battery voltage would drop below 12.0 V with sudden loss of power steering.
So be careful if you drive it without alternator. If the power steering fails just before a bend you'll be surprised how hard it suddenly is to turn the steering wheel. This is a dangerous condition.
