i've got a problem using the ENC28j60 Breakout Board with my old Diecimila.
Which uses a ATMega168, right?
Using a newer Arduino Uno there is no Problem at all.
Which uses a ATMega328 with twice the memory.
I think that we can safely assume that the Diecimila simply does not have enough memory.
On thing odd i noticed was that the LED on Pin13 is slightly lit on the Diecimila when the Board is connected. That is not the case with the UNO.
Pin 13 is part of the SPI set of pins. You should not be trying to do anything (else) with pin 13. If only the Ethernet shield is manipulating pin 13, then the fact that the LED is one sometimes is OK.