Why can't I connect more than one Arduino Uno + Ethernet Shield to my network?
It would be most helpful to see the code you're using and to know more about the configuration of your network and the symptoms of the conflict – for example where is the web site running?

Some things to try:


Simplify your network. Eliminate everything but the Arduinos and the web server. See if that changes anything.
Run the command arp -a (assuming you've got a machine running something UNIXish). It will show you the MAC and IP addresses of hosts on your network. Look to see if the Arudinos are still there and if there are any devices that conflict with them.
Try to ping the Arudinos. Do they respond?
Use WireShark or tcpdump to monitor traffic on the network. Look for traffic to or from the Arudinos (by IP addresses and by MAC addresses).
Add some debug code to the Arduino sketch so that you can watch what they are doing (send it out the serial monitor). See if what goes on the wire matches what you expect (monitoring with tcpdump).