I have a V5 ethernet shield attached to a mega 2560 and it works really well. The 'official' arduino was modified especially to work with the mega boards, and at least in my case, does. The fact that you don't have a light on the router when you plug it in and power it up probably means the board itself is actually bad. The ethernet board will interact to a small degree with a router with only power supplied and no program at all on the arduino. Additionally, there have been reports of seemingly official arduino ethernet boards that were very different from the V5 cards pictured on this site; they even came in the cardboard box.
I recommend you contact the supplier, they'll probably work with you on this.