That transfer case can be really hard to shift when the wheels aren't moving. If the gears are lined up just wrong, then it won't shift until the truck moves a bit. I thought my transfer case was broken when I first got my truck, but I learned that I just needed to get the hang of shifting it. Try to avoid needing to shift it when you're stopped on level ground. Shift it when you're moving a bit if you can, or at least try to stop where there's enough slope to let the truck move a bit if you need to spin the gears. You might have a real transfer case problem, or you might just be getting to know your truck. I hope it's the latter!
There are two controls which engage the front axle:
1) The switch on the dash (it's actually an air valve) that lets you manually engage the axle.
2) A valve under the truck, which gets turned on by a plate on the transfer shift linkage when you shift into low range.
If the valve/linkage under the truck isn't adjusted right, then that's one way for the axle to either not engage automatically in low range, or stay engaged all the time. Or one of the two control valves might have an issue. Or the air plumbing, or a mechanical issue in the transfer case...
That valve under the truck is sometimes deliberately disabled, too, to make the front axle not automatically engage in low range. It wouldn't hurt to start your debugging by locating that valve under the truck and seeing if it's all set up right. If nothing else, you'll get to know your truck's innards better.
