Cannot directly connect Arduino Ethernet to PC
Network problems can be complex.  If these suggestions are not right I can change the answer later if other solutions present themselves.

If you are connecting two Ethernet devices directly you may need a cross over cable.

To test your connection with out using IP addresses, try to follow what is discussed in this answer where the MAC address is used on a Ubuntu system instead of the IP address.

You also might try using wireshark to monitor the Ubuntu box's Ethernet port.