If it's 8 months old, it is under warranty.
When you connect it to your computer, does the shuffle's light come on at all? If so, what does the light do?
As a test, shut down (power off) your computer. Disconnect all USB devices including hub, except for standard keyboard and mouse if normally used. Do this to reset the shuffle
Start up the computer, run iTunes, and connect the shuffle to a direct USB port on the computer.