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!
Plugging the charger in and then turning the phone on works for me.