Grrrr (Defective iPod Touch)

So, I ordered my iPod in the middle of September. It finally arrived in the mail today...a shiny new 16 gig touch. I eagerly plug it into my computer and sync it up. When it's done, I pick it up, slide to unlock, and eagerly press my finger on "music".....only to have it not respond. Confused, I touch Videos and iTunes, only to have it do the same thing. I go up and press calculator, only to find it works perfectly. It appears the bottom centimeter of my touch doesn't recognize touch! I tried reseting it, restoring it, going to an earlier firmware...everything before I finally called Apple. Their response? I can mail it in..but it will take another 2 weeks for me to get a new one, that may or may not have my personalized engraving! Ahhh...I paid 400 bucks for this thing..and I may or may not even get my replacement engraved???

What gives? Anyone else run into this problem?