If the 2000's still have Pulse Vacuum Hubs (PVH), it could be a couple things. Once in a while on mine, they seem to get "out of sync" and one engages but the other doesn't, or when I go back to 2WD, one stays engaged. Try putting it in 2WD and then park it and crawl underneath to see if you can rotate the CV shafts. The hubs disengage via vacuum pulses and the transfer case is electric, so in 2WD, you should be able to freely spin the halfshafts while the vehicle is parked when the hubs disconnect. You can see if various drivelines are engaging to try to narrow it down. When I had a hub go out a few years ago, basically all the power would go to the wheel not engaged and it didnt have functioning 4WD. Another issue is the shift motor on the transfer case can fail. There are walkthroughs in the Tech Library for removing and inspecting the shift motor. One other possibility is a vacuum leak causing the hubs not to engage. Basically my understanding is the hubs work sort of like a clicking pen to engage and disengage, and if the vacuum isn't working correctly, the hubs won't engage. There's a vacuum solenoid under the airbox if you have vacuum hubs. When my hub went out, the light came on normally like yours, so you're going to have to do a bit of investigating. Good Luck.
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