I have a Samsung Galaxy Nexus 4G for Verizon Wireless and none of the methods suggested elsewhere in this thread worked for me, but the general approach is viable. Here are the exact steps I take to reliably cause my phone to power on.
1. Remove back cover to expose battery but do not remove battery.
2. Plug phone into any power source.
3. Watch screen: First, a battery icon with a lightning bolt in the center will appear. Then the screen will go briefly blank, and a battery icon that shows itself filling up will appear.
4. Wait a few frames of the animation, until the icon is full or nearly full, and briefly remove the battery, then reinsert it. The total time out should only be 1 second or so.
5. The battery icon should stay "stuck" at the frame of the animation which showed when the battery was physically removed. It may flicker a bit.
6. After about 10-15 seconds, the phone should power on.
I'm not really sure why this works in general, or why these particular steps are required for my phone, but if anyone is having trouble, please try it.