Just brainstorming here. Is it possible that with a battery severly depleated and/or with a poor cell, it could be acting as a "load" when the jump pack is hooked up, thereby taking some of the starting power available going to the battery. It seems a long time ago with I had to do a lot of "jumping" of batteries on an old car I had, when the battery was "really dead" I had to hook up the jumper cables and it wouldn't start at first, but then after I let it be hooked up for awhile and reved the engine on the running car it would start.