I just got my Droid 3 about a month ago, and I encountered the same problem when I put the phone to sleep for dinner. I tried to turn it back on with the power button, both with a short press and a hold attempt (30+ seconds) to no avail. I knew it had a substantial charge left, and didn't feel like taking the battery out, so I tried what came naturally, and it woke up a moment later:
Open slide-out keyboard, hold power button, and mash a lot of keys simultaneously - phone wakes up to the standard unlock screen.
I can't say that will work for everyone, but it beats taking off the case and pulling the battery for those that do get it to work. Good luck!