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Sounds to me like the the battery isn't getting charged for some reason. Do you have access to a volt meter. If so, can you tell me what the battery terminal voltage is while the truck is running. We need to see a voltage reading of 13.5-14.5 Volts while the engine is running and charging the battery. If you get anything different, please let me know.
I am going to do a little more research. Your charging system check is spot on where it should be.
I am going to dig a little deeper to see what I can come up with.
In the mean time will you answer the following questions for me.
All connections from the battery to the alternator are tight?
Is there any check engine or other warning lights illuminated?
Have any accessories been added to the vehicle ie. radio, off road lights, trailer wiring harnesses etc....