Arduino mega 2560 how to connect to the ethernet shield.

If this is the only thing connected to that ethernet port, is the ethernet port in the laptop assigned a 192.168.1.x/24 ip? No subnet conflict with your wifi? No web proxy settings?

It could be a routing problem with your main internet connection. Is that wireless? Any chance of using the wireless router with the shield connected to it?

edit: If you think it may be a proxy setting, change the server port for a test. Use port 8088 in the shield, and
http://192.168.1.2:8088