My vista compaq computer won't recognize my ipod nano 3rd gen. Help!

I have a “new to me” ipod nano 8gb 3rd generation. I have reset the ipod and have gotten my vista laptop to recognize it. Now I want to my desktop to recognize it cuz that is where all my music is. I have reset ipod again and removed and reinstalled latest itunes. Desktop is still not recognizing it. Help!