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Can you supply a diagram of how you wired up the relays and how they connect to the Arduino?
If you can ping it sometimes and not others, make sure that you are feeding the correct voltage to the network board. Some boards use 3.3V, other boards use 5V. Also try replacing all of the jumpers connecting the board to the Arduino with a fresh set of jumpers. Lastly, try a different network board.
How many outputs do you need?
How many total outputs do you need?