Hyundai Repair: 2006 SONATA 4 CYL WITH 78000 MILES, sonata 4, air bag system

Question
AIR BAG LIGHT CAME ON WHEN I PUT A ROLL OF NEWSPAPER UNDER THE DRIVER'S SEAT. I TOOK THE PAPER OUT THE LIGHT STILL ON. I TOOK A LOOK AT IT AND MOVE THE SEAT BACK AND FORTH AND WIGGLE THE WIRE UNDER THE SEAT , UNPLUG THE WIRE AND CONNECT IT BACK ON STILL STAYS ON.

Answer
The air bag system is set up so that, for most faults, the warning lamp will stay on even after the problem disappears.  

I'd recommend taking the car to the dealer (or other qualified shop) to have it checked.  Most likely, the issue isn't related to the newspaper at all and a repair is needed.