Some motherboards have a special "always-on" USB port... usually colored red or orange. This port will be on even when the PC is shut off. Also, there may be some software that has to be installed or a BIOS setting that has to be changed to activate the always on port. But I would first check if you have a special colored USB port that is on when the PC is off. (may be on the back of the PC)
Was this a pre-built PC?