Make sure that your HP laptop has all the latest driver, firmware, and BIOS updates via the laptops support page.
Also make sure that you have the latest Windows updates and patches installed.
Have you ever been able to successfully use/sync the iPod with this laptop before?
All of my drivers and Bios are up to date and I update every time there is a new update. I am trying to sync this iPod for the first time but I have a 2nd gen touch that works just fine on this laptop. the mini that I'm trying to sync to this laptop syncs to another laptop just fine, that pc is a vista system also.
Have you previously installed any other USB devices on the PC? Have you tried another known working USB cable to see if that makes a difference?
Since it connects okay with another PC, try restoring it in iTunes on that PC and then try to reconnect it to the original laptop you are wanting to sync it with.