I'm not sure how much those shuffles go for, but I do know they are the cheapest ipod apple sells (no screen -- wtf). If you can convince whoever bought it for you to give you the receipt, you could return it for a model that may not be defective (if it is defective, maybe it's just stupid). OR return it for store credit and buy other stuff. OR try to get some money out of it and invest in a Cowon iAudio U2 1GB mp3 player. This thing owns. I've dealt with them twice, and it kicks ass.
http://www.cowonamerica.com/products/iaudio/u2/
So iTunes doesn't transfer your music to the player? I seriously think it does. As annoying as I'm going to sound, sit down with the manual to the ipod, and read allllll about it. take it with you in the shitter. Specifically look to what it says about transfering music to it from a PC. Maybe there is a certain folder it has to go into, or maybe it needs some sort of index file.