One reason you may be experiencing this problem is that you are running the latest update of the router's firmware: 1.30EA
EZ-Internet may not support this firmware version.
As henkg has mentioned, it is possible to connect to the internet through he router's interface and set the port forwarding rules manually.
However we'll do our best to upgrade EZ-Internet as soon as possible so you don't have this inconvenience in the future,
I also have the same problem, and I have spent a full day in order to get the DS to work behind the router. I can reach it locally, and I have checked if the ports are open and they are. Still some problem. But I am getting confused since you are stating that the latest firmware for the Dir-655 router is 1.3, while when I look at my current firmware for my router it is 2.0.
Just at people have said before me, I bought Synology since it was easy to connect. And yes, it was, if I take away the router. Obviously that is not an option!