If the airbag light is on, chances are you'll need a new airbag computer. If anything goes wrong with the airbag system, there's a thermal fuse with a heating element in the computer that will permanantly blow, sort of committing "suicide" to shut down the system and prevent an accidental deployment. The only bad thing is, if you're in an accident- you don't get an airbag.
You're kind of stuck with getting it fixed at the dealership. You could try getting a computer from a junkyard and see if that cures it. But, if it's something outside the computer like the clockspring switch (keeps wire to airbag from getting twisted when steering wheel turns), a new computer will blow too.
Dealerships generally won't sell you airbag parts, due to liability concerns. They have to fix it themselves.
skymarshal you have to be ****tting me. I can't believe this otherwise I would have not disconnected my connectors when I removed the dash to do my heater core. There has to be some other way to fix this. When I start my car up it beeped a few sets otf times, then stops. light stays on. now I disconnected plugs and light is on. I gave up....