I've had the same problem. I had to cut the end of a usb cable, strip back the power cables inside then wedge them between the battery terminals and the phone's terminals, keeping the correct polarity of course. Then plug the USB A end into a computer.
Completely dodgy but it worked to get the phone started. The problem returned a day or two later though.
I would just glean all your stuff off of it when you have the chance then get another phone! It's always given me trouble!