engine shuts up when the battery is disconnected

If you have a multi meter you can check your alternator . With the motor off you should have a voltage of 12.6 min start your truck after starting it should be at at least 13.8 to 15.3 volts (engine running, lights and accessories off). If the voltage is less but comes up when you increase the rpm you may simply have a loose alt belt. If its less with revs your alternator is your problem these voltages are taken at the battery. If you don't have a multi meter another quick test is to turn the radio on and rev the engine. Tune your radio to a low number on the AM band with no music. If the radio whines or goes fuzzy whenever you hit the gas, the alternator is quite likely the culprit.

Hope this helps