if the problem was in the t-case; changing the fluid "might" do some good for the clutch pack.
from what you have described: the front prop shaft turning when in full 4wd mode, the front axle actuator working....the next step would be mechanical inspection of the front diff. I think that is where you problem lies.

 

I agree "might".

 

I notice a whining sound when I accelerate. The sound is very similar to all terrain tires on pavement. IT stops when I let off the gas pedal. It's not real loud, but noticeable. I'm not sure where the sound is coming from or if it's related


Today I peeked in behind the driver's front wheel and I noticed the differential is wet and appears to have been leaking.

 

I just realized that there is no "4X4" indicator light that lights up in my instrument cluster. Is there supposed to be one? I was looking through the owner's manual and it showed an indicator that I haven't seen.