Click on the Apple Menu (that's the little apple in the upper left corner of the screen), and select System Preferences. Now you should have all the computer's preferences available on one pane. If not, click on the little "light switch" button-this is the Show All option.
Now, somewhere in the window you're looking at, you'll see a section called Internet and Network. Select the Network icon to get the Network setup screen.
Now select the Built In Ethernet option from the Show menu at the top. You should have a selection called "Configure IPv4" and it should be set to Using DHCP. Click the down arrow for this selection, and choose the Manually option. Now you can enter your own manual IP address and subnet mask, gateway, etc.-they should be the same numbers you used on your old PC. In this case, your primary PC is sharing your connection, and it is probably your gateway.
If you're using a DHCP server on your primary PC, this shouldn't be necessary, but you may need to use the Renew DHCP Lease button to get the Mac to get a good address.
Finally, why not use a router? They're cheap, single purpose boxes that offload a lot of messy details from your computers, and let you concentrate on computing with them.