If you haven't already done so, try connecting the NAS device to the router using an ethernet cable, then restart the router.
Let me know if the port light on the router starts flashing after it has been rebooted...
The flashing is an indication that data is being transferred, so it is normal for the light to flash when the computer is connected.
A better test would be to try to ping the IP address of the NAS when it is connected to the router - can you try that?
Are you using a Windows PC or a Mac?
If you don't know the IP address then try pinging the Host Name (normally printed on the NAS) and the command prompt replies will show you the IP address.
With the NAS connected to the computer, can you access its settings page?
Let me know if it shows the IP address there?
Ok, we can continue tomorrow.
Do you have anything stored on the NAS yet?
If not, could you try a complete system reset on it?
Ok, I will check if the other experts have any further idea on how to proceed with this...