Welcome to the board! You're in for a fun ride!
There is supposed to be an interlock that prevents the transfer case from going into 2wd low range, but it wears out quickly. That's what you've found between neutral and 4wd low. It's OK to use it under certain circumstances, such as driving in a parade where you want to go slowly but don't need much pulling power. Remember that you can apply twice as much torque in low range, and all of it is going through only the rear driveshaft, so be conservative with the application of power.
4wd high range is there, but sometimes it takes a little doing to get to it. The cogs have to be lined up right, and if you're just driving down a dirt road everything is turning at the same speed so it can be a while until there's enough differential to line things up. Just roll forward while pushing on the lever and it should go in.
You mentioned "the front driveshaft stays free" which suggests that you have unlocking front hubs that look something like this.
DSCN0294a.JPG
They unlock the front hub from the front axle to save fuel and wear on the front drive components when 4wd isn't needed. If they're unlocked you can't get drive to the front wheels, so you might think you're not getting the transfer case into 4wd high when you really are.
And one more quirk of that transfer case, a Dana 20 by the way, is that it often doesn't want to come out of 4wd low. That's because there's usually a slight difference between the front and rear wheels that creates a bind in the transfer case. If it doesn't want to come out, drive slowly forward in a straight line while jerking up on the handle. If you still can't get it out, drive backward and jerk on the handle. Eventually you'll get it to come out.