Rear wheels not engaging what can I do to troubleshoot the awd?

There are quite a few things that can cause this. It should be as simple as a software upgrade to the differential electronic module or as expensive as an angle gear.

I don't know of a safe way to check if the driveshaft is turning without raising the car off the ground, but that's where you'll need to start.

If the driveshaft turns but the rear wheels are not engaging then the codes will need to be pulled and the system diagnosed.

If the driveshaft does not turn then the angle gear or the collar that connects the transmission to the angle gear is stripped

The only thing I could tell you that might actually help right now is... Remove the battery cover in the rear of the vehicle, it's under the load floor. Disconnect the battery cables and leave them off for two minutes. Reconnect them and drive the car. If the AWD engages then a software upgrade may fix it, or there's an intermittent electrical fault in the sensor system.
Volvo has a complimentary (free to the customer) software upgrade available for all cars sine 2001. Some dealers do it, some not so much. Ask for it, most of the software packages I've seen include the updates to the differential electronic module (DEM) if they have anything available anyway.
Hope this helps and good luck.

check the operation of the centre diff and the drive mechanism and oil levels.

No 4X4 switch on the instrument panel ?
Automatic Transfer Case
The single speed automatic transfer case system shifts automatically from rear wheel drive to four wheel drive when the transfer case shift control module (TCSCM) senses the difference in rotation speed of the front propeller shaft and the rear propeller shaft . Two vehicle speed sensors, one located at the rear output shaft area of the transfer case, and the other, located at the front output shaft area of the transfer case, send front and rear propeller shaft rotation speed information to the TCSCM.
When the front and rear output shaft rotations remain the same, the TCSCM sends pulse width modulation signals to the encoder/motor to keep the transfer case in rear wheel drive. When the front and rear output shafts rotations are different, the shift control module sends pulse width modulation signals to the encoder/motor to engage the transfer case into four wheel drive.
The system will automatically transfer a percentage of torque to either the front or rear axles as required to stop all wheel slip. When the front and rear output shafts rotations return to the same speed rotation, the shift control module sends pulse width modulation signals to the encoder/motor to position the transfer case back into rear wheel drive.
When the transfer case is engaged into four wheel drive, a lamp indicator on the instrument cluster will light. The automatic transfer case system is completely automated, no transfer case control button switching system is required.

Do you know what DTC'S - diagnostic trouble code's are ?
Auto part stores can't read these , your best bet take it to a qualified repair shop . One that has the knowledge an diagnostic equipment .
DTC C0300 Rear Speed Sensor Malfunction
DTC C0305 Front Speed Sensor Malfunction
DTC C0308 Motor A/B Circuit Low
DTC C0309 Motor A/B Circuit High
DTC C0310 Motor A/B Circuit Open
DTC C0315 Motor Ground Circuit Open
DTC C0374 General System Malfunction
DTC C0376 Front/Rear Shaft Speed Mismatch
DTC C0550 ECU Malfunction
DTC C0611 VIN Information Error
DTC C0895 Device Voltage Malfunction
Without proper factory service an repair info. an diagnostic tools

Depends on the model, if it is all wheel drive it should have AWD on the back window.
The Honda CRV uses very smart technology to have AWD. Let me explain it simply. The CRV is essentially a front wheel drive car, but there are sensors mounted on all the tires that sense slipping. If the computer determines the wheel is spinning faster than the other ones, it uses hydraulics to engage the rear end differential and presto..All Wheel Drive. You do nothing, no switches, no levers, the computer does it all for you. If it is indeed AWD, you can look under the car to see if you have a driveshaft going into the rear differential (axle)

Please vote if this helped! Thanks, Mike

IT'S AUTOMATIC! If there is a "TCS" or "Traction Control" button/switch, then leave that engaged at virtually all times. That year of the Saturn Vue did not come with 4WD (4x4); it offered AWD (all-wheel drive) which automatically supplements its traction control system (which was standard on all trims of that model in that year). AWD tranfers up to 50% of the power to the rear wheels when it detects wheel slippage. One up side (or pro) to having AWD is that you can use it on pavement. 4WD is generally too aggressive for that.

awd means all wheel drive,so toyota highlander was front/rear 50:50 fixed torque split

motor on transfer needs tested and replaced

IF IT IS NOT ENGAGING AND THE CHECK AWD LIGHT IS NOT COMING ON I WOULD SUSPECT THE AWD MODULE IS BAD IF THE LIGHT IS COMING ON THEN YOU NEED TO GET THE DTC IT COULD BE SEVRAL THINGS MOST COMON ARE REAR SHAFT SPEED AND FRONT SHAFT SPEED SENSORS REAR SENSOR ALSO CONTROLS THE SPEEDOMOTER COULD BE A BAD ENCODER MOTOR OR A BAD TRANSFER CASE

I have the same car. Mine is automatic. What is yours?

Possible scenarios:

1/ Is the FWD on the dash panel lit up? This will tell you that only the front wheels are engaged without power to the rear wheels. The manual tells you if you have a flat tire in your car, you have to make it into a FWD by inserting a fuse in your fuse box. Check and see if the circuitry isn't shorting out your awd which is making it fwd.

2/ Because the car has open diffs in the front and rear axles, you (or your friend) might see only the front wheels spinning and not the rear wheels. The power is transfered to the wheel with lowest resistance. With the front wheel spinning, one of the rear wheel(s) should also spin. Might not be a solution but maybe you can't see the rear spinning wheel because it's spinning on the other side.

usually normal condition for sharp turning, check and see that all tires are the same size. if you replaced two on front and not on rear this may be your problem