I don't know what you are refering to when you said that you have a ethernet connection on the back of your harddrive....

There are converters that you can use for connectiong to the router through the USB port on your computer. The problem is that they are designed to be a temporary fix....it would be best to buy a pci card and install it...

I use this to connect customers computers to my network so as to download updates quicker than their dial up modems.
Newegg.com - TRENDnet TU-ET100C 10/ 20/ 100/ 200Mbps USB to Ethernet Adapter 1 x RJ45 - Network Interface Cards

I buy these by the dozens as they are cheap and easy installs.
Newegg.com - ENCORE ENL832-TX-RE 10/ 100Mbps PCI Fast Ethernet card 1 x RJ45 - Network Interface Cards

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The propper connection proceedure is....

cable to modem Cat5E connected to router (hardwired or wireless) Cat5E to computer1 and Cat5E to USB adapter or new ethernet card to computer 2

The only differnce to this is some ISP providers supply their customers with a combination modem/router....which if possible try to avoid and supply your own as those provided by from the ISP are usually tuned way low and unaccessable by the end user.