So basically you said, you have a computer connected to the internet, through a hard wire connection to your modem, and you want to basically use that same internet connection on two devices, the one computer you're using it on right now, and your HP mini netbook/laptop. If I'm right, and that's the case, then if both devices have a Wi-Fi card, and the one you currently have connected to your cable modem uses Windows 7, just create a bridged connection between you're ethernet card and your Wi-Fi card (and use that Wi-Fi, on the HP mini). To do this, go into your "Network and Sharing center", and then on the panel on the left hand side of that window, click "change adapter settings". Once you're there, select the one Ethernet network adapter you're using to connect to your cable modem, as well as your Wi-Fi card, then right click on either one of them, and in the context menu that appears (note: if you're not an administrator, you will need the administrator's password to do this, as it would be a system-wide change) click bridge connections.