Keep the leads from the other vehicle on your battery for a period of time before starting your truck. Check the battery to ensure there is sufficient charge in it (at least 12vdc) to keep the vehicle running. Get your truck started and then pull the leads from the other vehicle. Check the voltage at the battery. If the voltage continues to drop at a slow pace while it's running, the alternator is most likely bad. Pull it from the vehicle, take it down to the parts store and get it checked.
Also, ensure the battery posts and leads are completely free of corrosion. If it isn't, the battery more than likely won't charge. Your issue lies in the fact the battery, whether completely new or the old one, is not getting charged. It is either the alternator not charging it, or there's no way for the charge to get to the battery due to corroded connections.