My vehicle was moving then later indicate neutral and stop I try to engage the gear but the vehicle won't move why

No it doesn't. Any neutral safety switch is to stop a driver from starting a vehicle while said vehicle is in any gear other than P (park) or N (neutral) so the vehicle doesn't just start moving after startup. This doesn't effect the gears any whatsoever. Early US model vehicles had the neutral safety switch on the steering column and was connected to the shift lever. Late model automatic trans vehicles have this switch mounted directly to the transmission shift rod at the trans and mounted to it.

gears slipping out will be indicated by the gear lever jumping into neutral.This can be from incorrect rear engagement from a loose worn pivot in the gear lever tower or something stopping the gear lever from moving properly.. Clutch problems are indicated by --going to the floor. crashing 1st gear, engines rpm s climbing without an appreciable vehicle speed increase. If there is a fault in the gear box it will be only in the gear engaged (missing teeth-chipped ) and not all gears. If it is a bearing then there will be no noise in 4th gear
Boxes are repairable as mostly it only needs that faulty part to be replaced

Locate neutral on transmission and connect shift linkage with indicator in neutral. Then make sure cable sheathing is not moving when you move shift lever, only the cable shouid move

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the key tumbler may be defective or the shift lock mechanism, do you have to put your foot on the brake in order to move the shifter without the key in the ignition? car willnot start does the lights come on do the accessory work lights, radio, can you shift from park neutral does the vehicle go into neutral have some one push it to see if it moves you may want to check the neutral safety switch or the gear indicator

TRY NEUTRAL ON THE COLUMN THEN MOVE SHIFTER ON FLOOR IN 4WD.I THINK YOUR TRYING TO MOVE SHIFTER ON FLOOR WHILE ITS IN DRIVE.

Ok, I guess its going to be a not too obvious solution then. All we have to do is find it...
1.What type of gear shifter is in your truck. Column or tower
2. Is the tail shaft turning when you try to move the vehicle
3. Does the vehicle try to move at all
4. Is there any noise from the gearbox or clutch area
5. Are you certain the clutch kit was the right one
6. Did you try the clutch plate on the gearbox input shaft spline
7. Is the release bearing clear of the pressure plate fingers.
8. Does the release bearing carrier slide freely on the retainer on the front of the bearbox, and did you apply lubricant here.

make sure shifter is not coming apart could have loosened up.

sounds like your flywheel

Jeep transfer cases are designed to be engaged when rolling from 3mph and up...low range should only be selected at low speed (around 3mph). Don't attempt to shift unless vehicle is moving...gears will not mesh properly. Try to find a manual to get the specifics of all variations of using the shift combinations available. (many times can be found in the gloveboxes of vehicles in scrapyards...just ask!

As far as I know the procedure should go something like this...

Stop the vehicle, engage the parking brake and if applicable, get out and turn the hubs on the front wheels from Free, to Lock.(You may not have these on a Suzuki, they may be auto-lockers)

Get back in the vehicle and put the transmission shift selector into Neutral.

If you have a manual transfer case, move the selector-shaft to 4x4-High, or 4x4-Low -- whichever is desired. Now, putting the vehicle in gear with the transfer case is sometimes somewhat difficult. As long as the vehicle's transmission is in neutral, don't worry, the gears inside the transfer case are big and beefy -- Don't be afraid to be rough -- Again as long as the transmission is in neutral. You may also have to disengage the parking brake and slightly let the vehicle roll forward or back with your foot-brake to get the Transfer case to lock into place.

Once 4x4 of the selected High, Or Low range is selected, usually indicated by the vehicle jerking slightly with a slightly loud clank/thud. Move the Transmission selector out of neutral into your desired gear (Drive if Automatic, if Manual, whichever gear you pull out from). and voila! You should now be in 4-Wheel-Drive.

To disengage 4-Wheel-Drive. Just reverse the steps.