Try switching to another USB port(s), perhaps one on the back. Not all USB ports carry enough amperage to power or charge things. The USB specification that manufactures must meet is about high speed data transfer, not about powering or charging external devices. For various reasons not all USB ports carry enough current to power or charge external devices. I believe your camera was designed to obtain it's power from the USB cable when pictures are being downloaded.
If changing the USB port you are using doesn't solve the problem, there is a good chance your USB cable is bad- replace it.