So it sounds like this is the first time you are trying to use this iPod shuffle with this computer... It has not previously worked.
If you have been trying to connect the shuffle to a USB hub, I would connect it to a direct port on the computer. And if you have not already done so since installing iTunes, do a shut down (power off) of the computer. Use this procedure to reset the shuffle
Start up computer with shuffle NOT connected. Run iTunes. Connect shuffle.
If that does not help, you should also try disconnecting ALL other USB devices, except for a standard mouse and keyboard. This is in case there is some USB device conflict. Then, connect the shuffle to a USB port that is directly on the computer.
If that does not help, and you have an Apple Store nearby, I would make a reservation at the Genius Bar to have the shuffle looked at. If it is defective, you can see about getting it replaced under warranty.