There is a way, but it's a PITA to get it to work. I had to do it until my replacement power button arrived.
You put the battery in. Then you plug in the usb while it's plugged into a computer on the other end (I don't know why it doesn't work with an ac adapter but I could never get it to work with one). Wait for the charging animation (not the picture with the bolt, but the actual animation where it looks like it's filling that comes after). Yank the battery mid animation. Put it back in before the animation disappears. If you're lucky, within a few seconds you will feel a vibration and the the phone will begin booting. If not, try the process again.