That....should not be possible. Yet here it is. The fact that it was low on oil concerns me and in internal damage to bearings, carrier spider gears and shaft, diff-loc friction plates and cage...ect. Equaling concerning is the black gritty fluid found in the rear gear case. That should be clear tractor hydraulic oil or wet brake fluid. It being in that state means not only serious neglect, but burning wet brake friction disks.
Lets get back to the front. For the back wheels to spin while the front is locked says the 4wd coupler must be at least disengaged enough to uncouple the drive shaft from the pinion. For everything forward of that to lock like the brakes are on, then releases when sitting a while says there is some force remaining after shifting that takes a while to dissipate. Kawasaki's system requires motion for the actuator controller to operate. It must get at least a 2mph signal from the speed sensor in order to make the actuator rotate. You can actually shift in and out of 4wd anywhere between 2 and 12 mph. Just do it with no power on or off the throttle, a neutral power state.
As for the locking I am going to guess a little here...its either the front brakes not releasing pressure back to the master..as in overfilled, seizing wheel bearings or outer CV joints...which is not very likely..but possible. Or, there is internal damage in the front diff of a kind that...well, differs from must I have ever seen. I think the pinion bearings are so bad that it is able to climb onto the teeth of the ring gear and lock. Somehow it slides off after sitting and resumes OK until 4wd is used again and is forced to climb back up the ring gear again. That's just my gut talking though. I think you are going to have to make sure its nothing from the wheel inward first, then pull the diff down and see what's going on. There is also a inner bearing retainer ring on the pinion that can be loose. It happens on the rear of many thousands of these but sometimes the front's do come loose. You can retract and remove the front driveline and see if there is and end play on the coupler which is attached to the pinion. Also and weird side or up and down play. That will tell you there;s something wrong there. A little play on the coupler's bushing to the pinion is normal. Good luck. Let us know what you find.
Lets get back to the front. For the back wheels to spin while the front is locked says the 4wd coupler must be at least disengaged enough to uncouple the drive shaft from the pinion. For everything forward of that to lock like the brakes are on, then releases when sitting a while says there is some force remaining after shifting that takes a while to dissipate. Kawasaki's system requires motion for the actuator controller to operate. It must get at least a 2mph signal from the speed sensor in order to make the actuator rotate. You can actually shift in and out of 4wd anywhere between 2 and 12 mph. Just do it with no power on or off the throttle, a neutral power state.
As for the locking I am going to guess a little here...its either the front brakes not releasing pressure back to the master..as in overfilled, seizing wheel bearings or outer CV joints...which is not very likely..but possible. Or, there is internal damage in the front diff of a kind that...well, differs from must I have ever seen. I think the pinion bearings are so bad that it is able to climb onto the teeth of the ring gear and lock. Somehow it slides off after sitting and resumes OK until 4wd is used again and is forced to climb back up the ring gear again. That's just my gut talking though. I think you are going to have to make sure its nothing from the wheel inward first, then pull the diff down and see what's going on. There is also a inner bearing retainer ring on the pinion that can be loose. It happens on the rear of many thousands of these but sometimes the front's do come loose. You can retract and remove the front driveline and see if there is and end play on the coupler which is attached to the pinion. Also and weird side or up and down play. That will tell you there;s something wrong there. A little play on the coupler's bushing to the pinion is normal. Good luck. Let us know what you find.
