I just got a brand new DIR-855 and am having the abovementioned problem. It first started with my DIR-655, I was using it fine for almost a year and suddenly overnight this problem happened, and it wasn't even due to a firmware upgrade. After weeks of trying to solve it, I decided to buy a new router, thinking that it might be due to my DIR-655, but it's giving me exactly the same problem, fresh out of the box.
My DGL-4300 works fine (so does my Linksys BEFW11S4), it connects within seconds of starting up. I can't figure out why my modem won't assign an IP address to the 655 or 855. I've tried all the usual stuff, power cycling, unplugging everything overnight, returned my 655 to Dlink customer service TWICE, etc., but nothing has worked.
I'm running a Motorola SB6100 Cable Modem on Starhub Cable Internet in Singapore. My 655 is on 1.21WW firmware and my 855 is on 1.11WW.
Any help would be much appreciated, thanks in advance.