iTunes is the ideal software for synchronizing the contents of the iPod with folders on your Mac or Windows computer.
However, if the iPod is not working, and not doing anything at all, then it may simply be damaged. Apple logo or not, iPods are still cheaply made Chinese goods with limited lifespans. If it won't charge, and it won't connect to the computer, then the port may be damaged. Or the wire may be damaged. I don't use an iPod, but I do have an iPad, and I believe they work the same way. The connector at the bottom acts as both charge interface and computer interface, for use with USB inputs.
If the wire is damaged, that's easy to fix. Buy a new wire.
If you're impatient, you can run to the local Walmart or Apple Store, and pay big bucks.
If you can wait a few days, get one off Amazon
for about $1.50 total. Yep, that's right, a buck and a half!
If that cheap ~$1 fix doesn't do the trick, then I would not waste time trying to repair the unit. If it's still covered by an Apple warranty, send it it. If not, just buy a new one. (I know, that's not fair, it sucks, etc etc. But it's really the only option left. Well, that and NOT buying an Apple MP3 player next time. But let's face it, cheap or not, iPod is still one of the best ones available.)
For new iPod Touch, look at both Amazon
(listing of iPod Touches here
) or the online Apple Store.
Consider refurbs, if buying from the Apple Store.
I'd be pretty devastated if my iPad ever conked out on me like this.