We can all kick this around till the cows come home but my advice, for whatever it is worth, would be to just go ahead and pick up an alternator.
The alternator may not cooperate and stop working in front of the automobile parts place of your choice.
You
are going to have to replace it... The rest of us all did when that happened to us.
Keith
P.S. If Tony says it is a blown head-gasket, just ignore him
