Hello.
This might be a bit late but you need to authorize the computer to allow it to connect to your ipod/iphone. When you connect you device in there will be an icon with the name of the device. Click the little arow facing to the right, right click on the music pannel and select tranfer purchases and when the window opens enter you password as normal and then another window should open saying "songs are not authorized" and press Authorize..

I think you can use Anisoft iTunes to iTunes Transfer ,an easy to use iTunes utility designed to help you backup/recover/transfer your whole iTunes library and media files. iTunes to iTunes Transfer is a simple way to keep your iTunes in sync everywhere. You can use it to backup your own iTunes library or synchronize multiple iTunes on different computers. The backed up library file is pretty easy to transfer to other iTunes, and it's easy to manage. So with this iTunes to iTunes Transfer software, you can manage your iPod/iPhone/... on different PCs. iPod /iTouch/iPhone transfer to PC

I think Aniosoft iTunes transfer is great since i have been using it for one year. so far so good.
i think it's worthwhile to use a program to transfer your iTunes library from one computer to another one since you requirement that the playlists,ratings should be retained. On the third-party program i would like to recommend Aniosoft iTunes transfer,with which you can not only backup your iTunes library but also in a proper way with the library's internal metadate,playlists,ratings and etc which you required. The backup files of iTunes library could be able to be recovered and restored later to any iTunes(authorized or not) W/out any change and risk in itunes'layout and arangement including its playlists simlpy through synchronizing it to the iTunes whenever needed.So try the Aniosoft iTunes transfer and it'll possibly work out for you.
more details at
http://www.ipodtocomputer.org

Go to store then autharize computer right click music then transfer purchases