It's actually really easy to remove ....and pretty straight forward. I've had mine out 2 or 3 times. But as mentioned above, you can probably remove the window lace trim around the sunroof and get at it that way. Your motor gear is probably toast. They are available cheap off ebay ...for ~ $15 bucks
HERE. If your motor doesn't move or whine, give the motor itself a whack with a large screwdriver handle or wood stick. Sometimes they stick internally. And check the power signal too in case it's a bad fuse, switch or connection.
If you need more access to the motor/gear, you can remove the two A-pillar covers and the front (upper) trim piece (and visors if needed) and it'll drop down more. Be careful, support it as needed, don't let it bend or kink. If you do need to remove the entire headliner, the key thing to keep in mind is most of the plastic parts pull out by hand fairly easily and have removable clips which are reusable if you're careful. The wise thing to do is to wiggle the plastic trim pieces as you put tension on them, which allows the retaining clips to slip through their mounting holes more easily. Then you shouldn't break any. Don't get rough or mean ...and it all snaps back together again. The H3 interior is really very serviceable. That's one area GM did good on, IMO.
So here are the headliner removal steps from memory:
1) Remove all the sill plates and rear door lower sill plate
2) Remove rear weatherstrip (top) piece ..at the rear door.
3) Remove seat belt shoulder pieces (front/rear)
4) Remove any screws on the large rear plastic window covers (the rear panels)
5) Remove screws from the upper (rear) headliner plastic trim piece (leave trim in place till the end)
6) Fold down rear seat and remove large plastic rear trim piece. Just pull it away by hand. Do the same with the pass side.
7) Pull down weatherstripping from top of the door openings
8) Remove both B-pillar plastic trims
9) Remove screw plugs (they say ABS), remove screws and remove A-pillar plastic trim pieces
10) Remove dome light and unplug wiring
11) Remove front and rear upper plastic trim pieces (support headliner as needed)
12) Remove upper handles
13) Remove front sun visors
14) Support headliner from sagging, bending or kinking!!
15) Remove sunroof surround trim.
16) Remove any other trim/screws, etc
17) Gently allow headliner to drop down. Support carefully while removing out the rear.
Extra: It's not difficult to remove the seats ...and the carpet at this point if you needed to (i.e. ..wet carpet).