Just posted a thread about this not a week ago after just fixing mine.
There is indeed a broken part. You have to remove the seatback to get to it. That task is actually far more difficult that replacing the part!
It's not entirely obvious how to get the seatback removed the first time, but once done, it's a cinch after that. The front seat cover by way of the springs and seat pads provide enough tension to hold the seatback in place. The front seat cover has a lip on each side that fits into a groove on each side of the rear of the seat...that's the seam you see running vertically on each side of the seat if you are looking at it from the back.
So the trick is to get a flat-tipped screwdriver and gently pry the lip from the groove at the bottom of one of the sides, then pull the lip away from the seat back as you go up. You only need to do one side as the offending part is easliy accessible at that point. It helps to push against the front seat cover to relieve the spring tension as you pull on the lip.
The part you need is about $17 at Fastlane (I bought two for insurance), and it is an integrated unit. Normally the plastic grip that holds the headrest shaft firmly is broken...so the motor can push the headrest up, but there is nothing to grab the shaft when the motor pulls the assembly down. Hence the "suspended" headrest problem.
Get the seatback off first, order the part and I'll fill you in on how to replace it...really simple 5-minute job!