I'm posting this to help someone else in the future. I spent countless hours to get this to work but nevertheless here it is. This is a two part video, that shows how to setup direct Ethernet communication between an Allen-Bradley Compactlogix 1769-L33E rev 21 and a Arduino Uno with Ethernet shield.
part 1
part2
In the video I send an array of bytes through an Ethernet TCP socket from the Compactlogix directly to the Arduino.