Front drive shaft wont turn on a 2001 chevy when locked in four wheel drive

did you turn the locks on the wheels, or check the fuses

There are 2 models here the push button will flash if the system is not engaging or disengaging properly . If front drive shaft is turning. That is with car raised and supported . if front drive axles do not turn then the axle actuator is not engaging axle shaft passenger side. Remove actuator and manually engage shifting collar with a screwdriver still does not turn then inner axle is twisted.

SOUNDS LIKE A BAD HUB TRY THIS TO DIAGNOSE THE PROBLEM

Put the transmission in park, set the parking brake and raise the chassis so one of the front wheels is off the ground while the other is still on the ground. When the transfer case is in two-wheel drive, the hubs should be released allowing the wheels to turn freely when spun by hand. If the axle shaft turns when you spin the wheel, it means the hub has not disengaged.
To check engagement, rotate the axle shaft backwards. This should lock the hub. Try turning the wheel by hand again. The axle shaft should now turn with the wheel if the hub is locked. If the hub fails to lock, the hub will have to be disassembled and inspected or replaced.
To check release, hold the axle shaft steady and rotate the wheel backwards. You should hear a click as the locking mechanism slides back out and disengages the hub. Rotate the wheel forward again and it should turn freely.
Another way to check the hubs is to raise the vehicle on a frame contact lift so all four wheels are off the ground. Then start the engine and place the transfer case in four-wheel drive and the transmission in drive. If the front wheels don't turn, look at the front axle shafts. If both shafts are turning, but one wheel is not, the problem is a bad hub on the wheel that isn't turning. If the front driveshafts are not turning when the transfer case is in four-wheel drive, the problem is inside the differential (broken side gears) or the transfer case (broken chain, shift linkage, etc.). If the driveshaft between the transfer case and differential is turning, the problem is in the differential. If the driveshaft is not turning, the vehicle is going to need repairs to the transfer case.
Hope this helps.

If your transfer case has an "auto 4wd" push button choice then the front shaft will turn all the time. This is due to how the transfer case is designed internally to provide that option.

the front axles have pinon gear box that the shaft from the transfer case goes to, it has a vacuum hose to it or a solenoid actuator check these for proper function this is how the power is turned on to the wheels.

the most likely cause is the front axle shift motor if bad your your front axle shaft will not lock in.if there is no shifting of transfer case there is also a electric motor that engages that in .

You have to have your front hubs locked in for four-wheel drive to work

If you can have the codes scanned in your vehicle it would be very helpful to you. If you have a code for the encoder motor sensor or the encoder motor itself on the side of the transfer case, this is where i would begin, quite common with the push button 4 wheel drive. Thanks for using fixya!! good luck

If your tires are on the ground the drive shaft wont spin, it sounds like your push button is either not connected or the one in the transfer case is jamed

The four wheel drive systems in these vehicles are simple. The push button controls the four wheel drive computer. The computer tells the encoder motor (on transfer case) to shift. When the transfer case shifts there is a vaccum switch on the transfer that is activated which sends vaccum to the accuator under the battery. The accuator pulls a cable to lock the front axle in. This covers all s series trucks and suv's with push button four wheel drive but not with auto or all wheel. Now to answer some questions. If your push button is lit up but will not go in to four high you should try to reset the four wheel drive computer. To reset pull the courtesy light and atc fuses for sixty seconds install fuses then cycle key on and off 5 times. If your transfer case shifts but your front end does not lock in check for vaccum at the switch on the transfer case in and out. If no vaccum out replace switch motormite number 49315 at parts store. If you have vaccum out check accuator.