Unresponsive To Touch

My iPad (32MB Wifi Only) is currently unresponsive to touch. I cannot even unlock it from the lock screen. I have tried the "hard reset" where I hold the home button and lock button down until the iPad restarts, and I've tried to restore the iPad from a backup in iTunes. Nothing I've tried has had any success.

The iPad doesn't appear to be frozen; the iPad changes orientation when I turn it 90 degrees, and before I locked it, double-tapping the home button brought up the search screen. It syncs with iTunes. It simply is not responding to any touch.

I've babied my iPad from the time I've received it, and I've been using the Apple case for most of the time I've owned it, so I'm not inclined to believe that this problem is the result of trauma.

The problem seems to have gotten progressively severe over the course of the past five days. Initially, I was able to resolve the unresponsiveness to touch by locking and unlocking. It worsened to the point where I had to do the "hard reset" (hold Home + Lock). When that no longer worked, I was able to resolve the issue by connecting my iPad to iTunes. It's worsened still, and now I can't resolve the issue at all - not even with a restore from backup.

I have some unscientific thoughts about the cause. I use Safari to browse Google Reader frequently, and the touch problem often manifests during this time. The problem could be manifesting completely at random and it just statistically occurs when I'm in Reader. At any rate, even when the iPad is working fine, Reader (in Safari) doesn't scroll correctly and often the Safari is unable to render the article summaries correctly. I wondered if the Javascript that Google uses is somehow causing an unseen exception in the iPad that leads to this problem.

Information:
iPad
iPhone OS 3.1.3
32MB Wifi-Only