Wired Router

I have two computers, one running on Vista and one running on XP. I tried using wireless routers and adapters and the older computer with XP seems to be having trouble so I think I am just going to use wired connections to use the internet on both desktops. I have a couple questions. My new computer has a spot for a ethernet cable in the back of the hard drive, but my other computer was connected though USB. Is there a way where I can buy a router and run the ethernet cable into my new computer and then a cable from my modem to my older computer through USB. Like is there a cable with ethernet at one end and USB at another? Also, if I hook them up with a wired router will I be able to use the internet at the same time on both computers?