AppleCare for the ipod is for one extra year (total of 2 years of warranty).
If you purchased a 3 year extension, it was through Sam's Club.
Contact AppleCare here: 800-273-2275 and see if they can help you figure out what's going on.
Alternatively, do as vazandrew suggested and take it to an Apple Retail store and have them look at it.
The phone number is incorrect for AppleCare.
If you need to contact them about your iPod, Mac or iPad
U.S. iPod, Mac and iPad technical support:
(800) APL-CARE (800-275-2273)
If you need to contact them about your iPhone
U.S. iPhone technical support:
(800) MY-IPHONE (800-694-7466)
The numbers above are if you are in the US and need to call.
International numbers can be found here
Sams Club has a better warranty but trying to file a claim is very hard. I've had this happen to me. I purchased a camera for $80. A year later, the buttons stopped working. I brought it to Sams Club to repair/replace.
They took the camera for 2 months and then informed me that the camera is too old and they can give me $25 credit towards a new camera. I told them I had the warranty but they didn't honor it.
Therefore, I'd go to Apple (first). Buy AppleCare and get a refund on your SAMS club warranty.
Just a heads up, both of those numbers will get you to the correct support. The ONLY reason for the different numbers is that iPod, iPad and Mac support lines are open from 9am-9pm (Eastern), and iPhone is 7am -12am (Eastern). So, if you want, you can call the iPhone line for your iPod touch or iPad using the iPhone number because it's all the same operating system.
My apologies about posting the incorrect number, it looks like I just got the numbers mixed up.