Was the iPod Touch only on the 4th Gen this last April? I bought my niece and nephew iPod Touches for Christmas 2011 and they were 4th gen. Was this a refurb? I guess not because you got it at Target and I thought only Apple could sell the refurbs. But I could be wrong.
My advice, take it to the closest Apple store and just tell them that the device won't hold a charge. They'll likely replace it with a new one. They may fix it for free, but more likely they'll replace it.
We had the same thing happen with my nephew's iPod touch, but we were 8 months past Apple's one year warranty. However, I purchased the iPods with my AMEX card. I've been an AMEX member since the early 90s and have never used the extended warranty....never had to.
Went to their website, and filed the claim on-line. It was so easy. I expected that I'd have to take the device to Apple, get an estimate, and then they'd either repair it or replace it. I was shocked when I heard back that they were simply crediting my account for the full $230 (device plus shipping/tax).
So, we purchased him a 4th gen refurb....just with more memory. He had an 8 gig, now he has a 16 gig. His sister still has her 4th gen iPod, and we didn't want to have hurt feelings by giving him a brand new one. By brand new, I mean...the latest generation. We wanted his new iPod touch to at least look like hers.
It was great to know that AMEX worked so well. One caveat, if we'd purchased a refurb to begin with, the AMEX extended warranty does not apply...at all. So, the refurb we bought him comes with the one year Apple warranty. By then he'll probably be ready to upgrade anyway.