The code works as do the examples included with the library. The problem is clearly with your network configuration and your failure to specify correct IP, subnet and gateway values. I'm deducing this because you're trying to ping and connect to the same IP address included in the library examples. You can't literally use the values included in the sample sketches. You need to assign values that are appropriate to you network environment.
- What operating system are you using on your computer?
- What is your computer's IP address?
- What's your subnet or netmask?
- What's your gateway address?
- How are you connecting your Ethernet Shield to the network? Is it connected to a hub/switch, or is the cable connecting directly to your computer?
- Which LED's light up solidly when you plug the network cable into the Ethernet Shield?
- Do the TX and RX LED's show any activity?