I suggest taking the alternator off and taking it somewhere else to have it tested but if you are getting a lower voltage with the truck running than with off then it suggests that the alternator is not producing any output as you are actually droping voltage while it is running.

If it were a pre computerized vehicle you could start the truck and then disconnect the battery and if continued to run then the alt was working but with a computer I believe you would/could cause damage to the system.

Def sounds like an alt problem though.

Val