My Droid 4 started acting weird today. I cannot power the device up normally. I have to hold power button and volume button, and that only works sometimes. I can power it up by sliding the keyboard out, too.
But then I cannot power it down by the power button, so it times out to shut down, and that drains the battery.
This sounds like a hardware failure, and, as the Droid 4 is less than a year old, you should be able to get a replacement under the 1 year warranty. The exception would be if the above happened after the phone fell in the toilet/went swimming with you/etc or some similar uncovered event.
One more caveat,Verizon will probably insist that you do a hard reset (Factory data reset) as part of their scripted debugging process. It's probably worth doing this anyway, just in case a misbehaving program is causing this issue. As you may be sending the phone back anyway, copy photos/music etc to separate storage (SD card/computer/cloud...)
So call Verizon and they will ship you a replacement (used but allegedly reconditioned!) phone.
(And yes, your replacement may well have issues, probably different. If so, keep returning. Eventually you will get one that is good enough!)