If you have broadband then that's what you want to use on the iMac. How does your PC currently connect to the broadband ie what is in between the PC and the phone socket on the wall? Is this PC the only other machine that you use with the internet?

For replacing the battery, it's on the logic board - take a look at the relevant Apple Service Source manual (tray- or slot-loading) here for details on how to access it. You may be better off just using Network Time if you're not confident opening the machine up though.