So I spent a bit of time on this last night and (hopefully) corrected it.
The symptoms were:
Some wireless devices could connect to the router such as a couple of laptops, a desktop and our Galaxy II phones.
Some devices could not connect to wireless, such as the Kindle's & Roku's.
Nothing could connect via hardwire, though I did notice that for about 4 or 5 seconds after each of the multiple router reboots, my hardwired desktop appeared to have a connection that could ping the router OK, then the connection just disappeared.
The N600 diagnostic tools are obviously very limited. There were a couple collisions adding up every minute or so, but nothing abnormal.
Steps taken:
Reset router to factory settings and reconfigured it. The hardwired desktop now had a functional connection however the wireless device connection status remained unchanged.
Did a continuous ping simultaneously on both the wired PC and wireless laptop back to the router. The wireless connection had a normal looking pretty constant <1ms response. The hardwired desktop however had responses bouncing up and down from 1ms to around 4000ms.
Disconnected all UTP cables from the router except for the desktop. Continuous ping responses remained unchanged.
Swapped out the patch cable going to the desktop, continuous pings returned to normal at a very constant <1ms. All wireless and wired connections returned to normal function. Had the the pings not corrected, I would have swapped ports on the router to see if that was the issue, and/or tried another NIC to isolate the cause.
So I guess the moral of this story is that a single bad device on the N600 router can cause it to lose partial functionality making it appear to fail without revealing itself in the router stats.