4x4 does not work

Most likely the control module assembly is the problem. It can be located under the dash and sometimes behind the passenger kick panel cover. You will normally hear a click noise when you engage the 4x4 and this click noise will indicate the location of the controller. You may not be able to access 4x4 hi if the lights are flashing but 4x4lo usually works.

If it is trying to kick in, then the fuse is not bad. There is a control box behind the left jump seat, if you have a extended cab, if not it may be behind the seat on the drivers side. This box should have a white or black button on the side. Push this button with the key on and it should reset the box. The 4x4 can get out of synch and it won;t work.
I hope this is helpful Good Luck

Assume for an instant that the transfer case is actually working. The next area to check is the hub actuators or that the front hubs are actually engaging to drive the wheels. Remember it requires both hubs to be locked in for the 4x4 to work or else if only one hub is locked then the front diff will work and all the drive will be to the wheel that is not locked in
The cost to check is really cheap. just jack the front off the ground and see if both wheels are engaged . Do this by placing in 4x4 and have a friend hold a wheel while you turn the other wheel or try to turn the other wheel. BY holding one wheel ,if the hubs are locked in then you will not be able to turn your wheel. Ensure that the transmission is in gear as if you are driving the vehicle.

solenoid may be getting intermitent power ..either broken /bad wire or connector or relay may be at fault.. parts store can give locations..

vacuum switch needs to be replaced.

The electric actuator sounds like it's not engauging. Hope this is it......

if your dash is not lighting up , check your tail lights
they are often on the same circut
if these are out you can be sure its a fuse

sounds like the punch solinoid in the front diff

try seeing if the cable going to the front differental is pulling in to engage the front axle?

Put it on jack stands. Start it up, put it in 4x4. Put it in drive. Both front and rear drive shafts should be spinning. Do they?