Aside from USB sticks do have any other usb devices (not the keyboard and mouse which both draw minuscule amounts of power from the ports) that you can test with?
Say an external USB hard drive, a digital camera, a dongle, etc? If so, try one of those and see what happens. If any of these aforementioned devices do not work then you definitely have USB port issues (motherboard perhaps?).
You might also want to try out a self-powered USB hub. Plug it into one of the system's USB ports and then plug the stick into one of the hub's ports. See if that works.