Here's what I think the problem is;
You have to push the switch to crank it. When you push the switch it connects the two battery systems. This is supposed to happen when you turn the key on also. So you have a blown fuse in the ignition to battery solenoid connection. The fuse is in the fuse box down by the driver's feet. Change out that fuse and your batteries should connect when you turn the key.
On top of that problem you have a draw on your engine battery. Over time it goes dead.
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