Check for a bad ground cable between the frame and the engine. You can try and use your jumper cables and go from the frame to the engine. I chased a problem like this on my 1990 chevy pick up. It would turn over like it had an almost dead battery. after hooking a jumper cable from the engine block and touching the frame it cranked over like crazy. also clean the battery terminals even tough you think they may be OK clean them anyway. Let us know what happens.
1990 28' Georgie Boy, 454, 4bbl, Thorley Headers, Recurved Distributor, 8.75 mpg. RVM 76