Any luck?
I re-read your original post...when you say "the car stays in 4x4 ... it goes off after while [10-15 min]", does that mean you've been able to shift the lever from 4H to 2H, but the light stays on? My initial impression is you couldn't move the lever back into the 2H position ("i have a hard time getting out of 4x4").
If so, that would open the doors to some other scenarios, but as before, the wheels should be in motion to engage and disengage the system. It is easily possible to have the lever in 2H and still be in 4H...it basically means you were in 4H, came to a stop, shifted to 2H, and parked it.
Also, not sure how I missed it earlier, but you posted pics and some thoughts about your
transmission fluid, and that you had it flushed through the radiator line. I assume you mean your transmission cooler...because it would be
really bad if you flushed it through the actual radiator.
However...the transfer case has its own fluid compartment. It
uses ATF, but a transmission flush does nothing for the transfer case. You should remove the fill plug (never remove the drain plug at the bottom first) and check the fluid. From the FSM:
