Then something is on pulling power from the battery. Any light on the vehicle or any relay that is stuck closed.
the alternator is bad
Your alternator is not recharging the battery and is defective.
Well it maybe that the battery is to small for the truck or the alternator is bad
If it is running on the battery only then that means the alternator is not charging the battery.
the diodes in the alternator have gone
bad alternator, bad voltage regulator, bad battery, bad connections.
Try jumping it off. If it cranks remove the + side on the battery. If it shuts off the alternator is bad .If it does not shut off clean the battery terminals . Have the battery checked at the Auto Zone.
As long as the alternator works and your charging system is correct, the new battery will start your truck and keep it running.
The answer is no . The battery starts you vehicle , the alternator charges the battery so if your alternator is bad your battery is not receiving a charge which will cause a "no start" condition.
Bad charging system? alternator or generator does not supply enough power to keep battery charged to operate accesories. Bad battery? can't hold charge.
bad alternator ? its not charging the battery
Start the truck then disconnect the battery if it's still running the alternator is good