I have a 2005 envoy 4x4 it will not go in reverse all so its stuck in 4 wheel low

SOURCE: 4x4 will not engage,lights just blink,and you can here clicking

The 4x4 system has a controller,or computer,called the Body Control Module and there will be stored trouble codes.To work on a system that's electronically controlled,you have to get the codes from the system.Every trouble code has a diagnostic route to follow to resolve the faulty component.I have read about Explorers having faulty door open/closed sensors.These set a code in the Body Control Module,and in the process,the BCM inhibits 4x4 operation,causing a no 4 wheel drive complaint.There is also an electric motor on the transfer case that can fail electrically or mechanically,along with speed sensors and fork position sensors that can give trouble.

SOURCE: 2000 F350 Super Duty Will not go into 4 wheel drive

I have recently had this problem with a customer. It seems the 4x4 low will only engage in neutral with the brake applied. And also check fuse. Then select drive and you will feel it lock in. Don't "goose" the fuel when attempting this.

SOURCE: wont shift back from 4x4 low, to 2x2

I also have a 2002 Envoy. Shifting to and from 4wh and 4wa can be done on the fly but shifting to 4wL has to be done stoped and while in neutral. Try that. Otherwise I'm afraid its a new computer for you. Its located under the left rear seat and you need a loan for one.

SOURCE: 2005 Ford F150, 5.4L V8, 4x4; The transfer case

Encoder motor located on the transfer case is usually the problem. It is the motor that shifts the transfer case.

Testimonial: "Will look into this and report .Thanks so much"

SOURCE: 2005 ford f-150...4 wheel drive will not

Operationally vacuum holds the IWE ( Integrated Wheel Ends ) out, and once vac is removed the spring engages the IWE.

Lift and support the front of the truck so the front wheels are off the ground ( take safety precautions, chock wheels, jack stands, etc )
Key on, engage 4x4 and try to turn the front drive shaft.
If it turns it is a problem with the transfer case.
If it doesn't it is a front axle engagement problem.

- If the front drive shaft does not turn :
Shut of the truck ( still jacked up, and supported ) remove the vac lines from the IWE. The spring should push the gears in, without the vac line on.
Check the vent line ( tube that is routed into the engine compartment with nothing attached to it ), for blockages.
If the vent line is clear, and with the vac lines off the IWE should be engaged ( both front wheels locked ).
If they lock, the problem is with the IWE solenoid not shutting off vacuum to the IWEs. There is a TSB on the 2004-2006 IWE solenoids, a newer revision has been made, and used from 2007 and newer MYs.

Here is a block diagram of the IWE system