W5100 Does not Show Up on Network

I am new to this Ethernet stuff, so bare with me. My board uses a W5100, but nothing shows up when I connect it to my computer using Ethernet. I have spent A LOT of time troubleshooting this issue, and I would like to confirm one thing. Using the factory default register settings, I should be able to just connect the W5100 to my computer, and it will start pinging back and forth and be identified as a network device . . . assuming I have the circuit set up correctly. I used a combination of the recommendations from Wiznet and the Arduino Ethernet shield schematic to make mine.

Not clear what you actually did. To make chip responding to outer world it should have its own address and network properties properly set - its IP address, address mask, gateway, reachable from your outer world - logically and physically, and some register bits set to allow pinging. At least what comes to my mind.