I had this exact issue, myself. I even went so far as to search for the issue here on the forums in the hopes someone had found a workaround with no luck. The most frustrating thing about the problem was that it was intermittent. Some days, I could go a whole day without issue. Others, it would start five minutes after using the phone first thing in the morning, and would not respond no matter what I did until I got so frustrated that i'd do a battery pull and reboot, only to have the touchscreen become non-responsive the next time I tried to use the phone. I will admit, the problem wasn't as frequent after the OTA, but still enough of a problem to be annoying.
My first time taking it into the Verizon store, I checked to make sure I was having a problem, but every time they would look at it, it would start working again. I waited for a few minutes at the store, and would get it to have the issue only for the problem to suddenly and mysteriously disappear once I got the attention of the sales clerk. The most frustrating thing about the whole ordeal, though, was the guy said "according to Verizon policy, unless we see the problem for ourselves, there's nothing we can do." Fortunately, I had better luck the second time, and was able to get a replacement.
I'm very careful with my electronics. Since switching to Verizon, every phone I've owned has had at least a hard cover. The D3 I'm using now also has a screen protector, and will be receiving a zagg invisible shield as soon as I have the money. I make it a personal rule to never intentionally do anything that will void the manufacturer's warranty at least until after the warranty has expired. As an example, I didn't root my D1 untill I was up for my upgrade, and won't be rooting this phone until this time next year at the earliest. And since switching to the Android platform, I only download apps using the market app on a stock device.
Long story short, I'm afraid I have no idea what caused the problem, or any solid way of fixing it. All I can suggest are a few temporary workarounds I figured out while it was happening to me.
1. After turning the screen on, try unlocking the phone until the screen turns itself off.
2. If step 1 fails, slide the phone open to expose the keyboard, wait for the screen to turn itself on, then try unlocking the phone again.
3. If that doesn't work, slide the phone closed, press the power button rapidly for several seconds, then repeat step one.
4. Usually if I got this far, I just did a baterry pull, but you may want to try combining steps 2 and 3 first (keyboard exposed, press power button repeatedly, then try unlocking).
On a good problem day, I never got further than step 2, and it'd work on the first or second swipe at that. On a bad day, I'd end up pulling the battery 3 or more times in the day, or just go the whole time without using my phone, all the while wanting to chuck the thing as hard as I could against the wall or ground. Unfortunately (or fortunately, depending on your point of view), this problem seems to be pretty rare so far. I hope the OP and others who are having this problem find something that sheds light on the issue, so others will not have to deal with the same headache.
