I was not able to take my playlist from my desktop to my laptop using my nano. I also have a touch, with it I can go from one to the other. Back your playlist up to another medium, such as cd or flash. Then open itunes on your laptop and import them. Whatever you do with itunes, keep a backup. Things do tend to dissapear sometimes.
I had problems with a game I purchased from itunes. It kept saying I didn't have the authority to use that game on my ipod. To solve that, (assuming you have already authorized the laptop) you have to go to STORE tab and deauthorize the computer and then go back to store and authorize it.