I have the same problem. It started after everything started crashing ever since OS 5! Took it to apple and they said they needed to reboot it and I would have to restore from a backup on my pc NOT through iCloud. Brought it home restored it, and five minutes later, poof! A line down the middle of the screen!
Went back to apple they just said, "Yeah, you'll have to buy a new one". Thanks for the great help! They told me they don't repair hardware problems! You just have to buy a new one.
My iPad was less than 14 months old. Should it not last longer? I only use it lightly. Several it seems have had this problem.