Paul
With the engine off and the key on the batt light should light. It could be a bad bulb (likely) or a broken wire. If you checked everything and you still have no charge (>13volts with the engine running) then the ALT is bad.
jeff
April
As long as the conductors are not corroded you can tape them up and you should be OK. Any corrosion will reduce the capacity of the wire causing heat and the possibility of fire.
jeff