The left LED is the connected speed indicator and shows a solid colour when connection and speed have been negotiated (it should be a solid colour all the time).
The right LED is the activity indicator and blinks when there is activity on the network.
The fact the left LED blinks says that it is trying to negotiate a speed for connection but appears to not be able to do so (LED off). This could indicate several things, 1) a bad cable, 2) a bad connection to the router, try another port (can be checked by using a switch ), 3) the NAS may be set to a fixed IP address that is on a different subnet (hold in reset button for 15 seconds at startup of unit to return to factory defaults), 4) the unit might be faulty.
There have been cases where, for some unknown reason, a router and NAS box will not work together. We have always solved this problem by using a simple 5 port gigabit switch available for under 20 euro (it also allows expansion of the network at a later date as well as positioning a wifi router in an optimum position).