I have a 2000 Grand Cherokee with a newly replaced 4WD transmission transfer case. Sometimes all four tires spin in the snow, and other times only the rear tires spin - the shifter is in 4wd high. When I put the shifter in 4wd low, all four tires spin all the time. I don't understand why the Jeep sometimes turns all four tires and other times only rear tires turn – why is this sporadic?

I'm not that familiar with the 2000 Cherokee's, but from my understanding, Part-Time will use only the rear wheels when traction is good, once traction decreases, it will engage all 4wheels (Part-Time should only be used on slippery surfaces, otherwise you'll experience "binding" on turns).

It's possible that your T-Case could be in a Part-Time mode, even though the lever is in 4HI.

I'm not sure how you shift your T-Case, but I do the following...

When parked, I put the transmission in neutral, then shift the T-Case into the desired gear, then shift the transmission back to drive.

When shifting while driving, accelerate & pull the T-Case lever sharply into the desired gear, hold onto the lever, & once you let off the accelerator, you should feel a slight bump in the T-Case lever (this tells you that the front axle has engaged or disengaged).

4Lo works just as you described (you should stay under 30-35mph in this gear)!

Hope this helps