A blown fuse would indicate an open and what you have is a short, but it only occurs when you try and start the engine ,correct? If that's the case I'd suspect the starter and in particular the solenoid. Replacing the whole starter, IMHO, is a waste of money. I would take the starter apart and check the brushes for wear and replace as necessary. A weak bendix usually will not fully engage or stay engaged and they are easy to replace. I would guess that you have a bad solenoid which, IMHO, is the weakest link in a GM system.