[mreid]

You can't say alternator just because the voltage doesn't come up when the engine is running. It's not the battery, but if it is older than five years I would replace it for peace of mind and avoidance of future trouble. That won't fix this problem.

There is a test where you jumper the regulator sensor wire to turn on the regulator to see if it works properly, but given your battery isn't charging at all and it hasn't overcharged, it probably is the alternator. However, the regulator is easier to change and cheaper and given the age of your car wouldn't be bad to have a spare on hand, I might change it first before the alternator.