Post this over at powerstroke.org. Someone there will know for sure what your problem is.
Have you tried installing a couple of good batteries on it? If one of those old batteries has a short between cells, it could cause the problem you describe. A couple of batteries that you know are good, plus all clean connections, will eliminate some guessing about battery condition.
I have had 16 Powerstroke 7.3's. If one battery is complete toast, you can get the problem you are describing, even with a jumper box or jumper cables.