On the alternator you should have a main battery positive, thats the big thick wire which should be fed all the time, not sure if this picks up from the + terminal on the starter and a thin wire which is the one for your battery warning light/ignition. Check that the thin wire has not broke off, if this is catching the body or any earthed point this can cause the light to stay on, otherwise i'm guessing the Rectifier in your alternators packed in. The light on your dash is needed to excite the alternator to charge, once the alt starts charging the thin wire becomes a positive and in turn the light goes out. The alts not that expensive to repair but you can pick em up new for around £40 + vodka n tonic. Hope this helps.