With a fully locking differential, does it slip first, and then lock up? I have a Trail Wagon UTV and I noticed today that after i had locked the differential, it slipped a little and then locked up. I'm beginning to think the company jipped me and threw in an LSD and claimed it was a locker...

 

Is it a luchbox locker or full carrier? The luchboxes will disenguage on any turn and sometimes it takes a bit of torque to lock them up again when their new. Some full carriers like the Eaton G80 wait for a full turn of the opposite wheel befor they lock both wheels.

 

no clue. it's a shift-on-the fly and you just pull a lever to lock it. also when climbing some steep hills, the wheels won't spin at all, but the vehicle won't move with the gas pressed in. is this b/c it's a small engine and doesn't have enough torque? it's kind of squeaky though so maybe the belt isn't catching

 

You would have to know what kind of locker was installed for us to answer. So your jeep didn't have this before, and has it now?
Shift on the fly...are we sure we aren't talking about a "center diff lock?" If they are vari-lok diffs, then they can move different speeds then lock, like an LSD.

Yes, if the wheels are not turning on a climb, you don't have the power to turn them. However, this is not because of a lack of power in the engine. It is because you need to be in a lower gear. If your transfercase has a low range, it should easily be able to spin the tires in first gear no matter what is going on. Doing it in too high of a gear is like taking off from a stop in a stick shift in 5th gear. The engine has no issue, it just needs proper gearing for the situation.