Are the arrows actually moving in a circle? That means it is thinking.
You don't need to install the new iTunes but you may want to download the most latest updater for the iPod itself from apple at it's website: http://www.apple.com/ipod/download
I'd restore the iPod to factory settings with the updater and then see if it works after that. It may need just a little kick start. You may have to put the iPod into disk mode first. Instructions can be found in my signiture.