There is another thread form a few months back, with some great pics of one of the reasons when it won't engage 4x4.
For me it was a combination of the teflon pads on the shift fork wearing out, and the splines on the shift collar got badly rounded so it would just ratchet out of 4x4 as it turned.
I tossed in a fork and collar from a low mileage F-150 with the same t-case, it's worked great since. Easy job, you don't even have to drop the t-case.
However, if I understand, it sounds like the shifter is physically hard to move into 4x4?