I recently bought an HP Officejet 6310xi All-In-One and i want to use and ethernet cable.?

You could buy a wireless router and connect each to a wireless network in the home. This will be your best bet, but will cost a bit of money. If the computers in the house do not have wifi cards at the ready, you can buy cheap usb wireless adapters for them. Then, just make a wireless home network.

I would presume, your house is using an Ethernet Wireless modem/Router. If that's the case, buy a wireless router, and connect your printer to the router. With this, you can place your printer anywhere in your home at your convenience. If you are using an Ethernet wired modem only without IEEE802.11 WIFI support, then, getting a wireless router would do you good because, now your home would fully support WIFI and connectivity would be an ease. In any case, i fear because you are unable to connect your printer to the modem in the first place, the idea above of using a router might not do it. In that case, buying a longer ethernet cable is a must for you. Or, connect your printer to the other computer (shared server or workstation that remains on), and shared the printer on the network. Go to network options under file and printer sharing, and enable it. (Go look into the control panel) Once the printer it connected to one PC, the other PC which is on the same network would be able to connect to the printer via the shared printer on the first PC. Isn't it great? Hope that helps