From your pictures it looks like the LEDs on the Ethernet jack are not lighting up, not even the green LED. This might be caused by a defective ENC28J60 Ethernet controller, or the 25MHz crystal. Both are pretty easy to source on Digikey or Mouser for just a few bucks.
But before you proceed, the ‘buttons’ not working might be related to the Ethernet jack. Can you be more specific about the ‘buttons not working’? Which buttons, and why did you think they are not working? Note that if you have the latest firmware 2.1.5, the button functions have changed. There is no longer a ‘test’ mode at start-up, instead, you can run a test program (using button B3) after the controller has powered up. For details, please refer to the user manual.