Why won't certain songs on my iPod play?

Hello, I have an iPod Touch version 4.2.1, and when I try to play certain songs on it, they appear that they are going to play, and then just skip over them. I purchashed them on my iPod, and when trying to sync them to iTunes they did not sync, and still won't play on my iPod. When downloading the two albums I bought on my iPod touch, they also made multiple albums with the exact same name containing 1 - all of the songs from the 2 albums that I just bought. I am wondering if there is a way to re-download these songs to either my iPod, or computer, and actually let them play. I am also having this same problem with a few of my songs that I used to listen to.

Thanks,

Acid