I just realized my 2000 Sportage 4x4 didn't work last week after getting stuck somewhere where I shouldn't have. From reading all of the previous messages in this forum and many others, I've realized this has probably been broken for awhile, I just didn't know it. My sportage has 99,100 miles on it and when we called the dealer to describe what was happening to the car, he couldn't believe this is the first problem with the 4x4 that we've had.
Anyway, I picked the car up today, and drove about a mile down the road to put gas in the car. When I parked it and cut it off, it started rolling backwards. It was in the park position but wouldn't quit rolling backwards. I re-cranked the car to pull it back up to the gas pump I had been parked at, but it wouldn't go into any gear, but instead made an aweful grinding noise, so I cut it back off. Even after putting the car in park, turning it off, and putting the emergency brake on, it wouldn't quit rolling backwards unless I also held the regular brake.
It sounds like the transfer case is broken. Question for you. When you picked up the vehicle after the repair was the transfer case in 4H and was the green "4WD" light on? If it was and you drove it on dry pavement chances are you broke the transfer case. You cannot drive a part time 4 wheel drive system in either 4H or 4L on dry pavement. If you do you'll bind the drivetrain and something will break. In your case it sounds like the transfer case gave out. The clue is the inability for the "Park" on the tranny to hold the vehicle in place. The transfer case is located AFTER the transmission and if it blows the park pawl in the tranny won't hold it.
Post back and let us know what they find. I'll lay odds the transfer case is gone.