In the 4EAT with the multi-plate clutch transfer system (not VTD), the AWD transfer clutch controls power to the rear drive shaft, only.
The front drive shaft (pinion shaft to the front differential) is permanently connected via the reduction gears to the output shaft of the transmission. If there's no drive to the front while there is to the rear, there has to be a problem in the front drive system; that is, at the reduction gears, through the pinion shaft, the front differential, and the two front half axles.
(Put differently, it's impossible for one or both rear wheels to be turning while neither front wheel is turning, unless there's a mechanical disconnect/break in the front drive train.)
The problem happens from a dead stop or standstill, seemingly not while already moving.
If there's a disconnect in the front drive (such as a broken axle), the AWD mechanism will sense this as a spinning front; it will increase the pressure on the transfer clutch, causing the rear wheels to push the car. Once the car is rolling, there's no way to know if the fronts are working or not.
Sometimes right side only.
The AWD system does not control power to each wheel (that is, side-to-side). It only controls power to the rear drive train, while the front is, normally, always powered.
Your car is equipped with a FWD socket in the engine compartment. It should be near the firewall on the passenger side. Insert a fuse in the socket. This should disable the AWD (prevent the clutch from engaging) and turn on the FWD warning light in the instrument panel.
With the fuse installed, the rear wheels should/will not get any power. Now, you can see if the fronts work at all. (If the front drive is intact, the car should move almost normally -- it would be the same as a front wheel drive car. This, of course, assumes that the transmission itself is working properly to begin with.)