As a test, shut down your computer and disconnect ALL USB devices. Do this procedure to Reset the shuffle
Start up computer with nothing connected, except for standard keyboard and mouse (if it's not a laptop). Run iTunes. Connect shuffle to a direct USB port on the computer. See if there's any improvement,
If the shuffle is now recognized, there may have been a USB device conflict previously, or maybe all of the devices connected at the same time overloads the USB bus (for power). An iPod charges its battery while connected, so it is a high-power USB device.