If you remove the transfer case shift motor and manually select 4 low you will know if the problem is the shift motor and other electronics etc.
I find myself wondering if you have odd sized tires or is someone changed the front diff and did't get the right ratio or something.
because you have the auto 4 wd mode, there is a clutch in your transfer case. When in auto mode your front end is engaged and turning the same speed as the rear but not actually powering the front wheels. When the computer senses rear wheel slip it engages the transfer case clutch, powering the front. If your tires or gears were wrong it would act stupid in auto mode.
I'd probably jack the thing up all 4 corners, very carefully go through shifting into 4 wd, auto mode, 4 low both with the shift motor and manually.
As you don't have any auto hubs and you have CV joints in the front, that pretty much is the end of my suggestions.
If you do jack it up and try all that, be very careful. Do not be under or in front of the thing when the tires are turning on the jackstands. And use jackstands, not blocking or a jack. That would be dangerous and stupid.