The first thing I would check is the 4wd button, you need to make sure that the switch is sending the signal to whatever actuator engages the 4wd. If you have a multimeter, you can test for continuity across the switch. The next step would be to trace the wires from the switch to whatever mechanism it activates. Look for damage to the wires or loose connections, maybe there is a fuse for the 4wd system, if so, check that. If you can determine that power is being sent to the 4wd actuator when you hit the 4wd button, then you need to check and see if the actuator itself is working. This will probably mean removing it and visually inspecting to see if it seems to be functioning properly. If all these things are working, you problem is something mechanical, could be anywhere. Put the quad on jack stands so that all 4 tires are off the ground. Put the machine in gear, and engage the 4wd button. Then see if you can hear any strange sounds when you try to engage the 4wd. This may help you determine where the problem is. I believe the entire front drive system is enclosed, so you can't really see any of the moving parts without taking the gearcase or the front diff apart. If you can't find any problems, you may just need to start tearing into the thing. A repair manual would be a worthwhile purchase, not only will it have instructions for tearing down and re-assembling your quad, it will have some troubleshooting tips as well. Good luck.
Yours truly, sincerelly, love always, Josh aka The DirtDemon.