start it up and pull the neg cable off the battery, if it stays runnin ur alternater is good. all the battery does is start the truck, everything else runs off the alternator, . i have seen one stay runnin with the cable off, but the alt wasnt puttin out enough amps needed to charge the battery.i just went through the same thing type problem with my runner and had a few bad grounds on the body and frame, u can try that, kinda sounds like a battery dischargeing.