Looks like you'll be need a wireless connection (recommended). You can route cables if you wish but that just looks ugly and be all over the place.
Here's what I would do. Purchase the following:
1 wireless router
D-Link DI-524 IEEE 802.3/3u, IEEE 802.11b/g Wireless Router - Retail
1 wireless USB adapter (I prefer the PCI adapter, but this one is plug and play through a USB port and is super easy to install)
D-Link DWL-G122 IEEE 802.11b/g USB 2.0 Wireless Adapter up to 54Mbps Data Rates 64/128-Bit WEP, 802.1x, WPA - Retail
Place the new wireless router near your computer or somewhere in your room. You're going to hardwire this one to the back of your PC using the supplied Ethernet cable. The USB adapter is for the other computer in the other room. That plugs in to a USB port.
The Earthlink modem should have an Internet port or a WAN port on the back somewhere. You're going to plug that cable (already attached to the WAN port to the back of the Earthlink modem) to the back of the D-Link wireless router, where it says LAN or something like that. Then connect the ethernet cable from the back of your computer's NIC to Port 1 on the new wireless router.
Power on both computers and you should have internet connection.