C6250 not detecting ethernet cable

> [...] I plugged one end of the ethernet cord into the ethernet port on
> the router, and the other end into the ethernet port on my laptop.
> However, neither my laptop nor the router detected it. [...]

   So: bad router, bad cable, or bad laptop.  Substitute or test the

pieces.

> I have tried three different cords, [...]

   So: probably not bad cable.

> [...] also tried connecting it to my desktop.

   So: probably not bad laptop.

> Am I doing something wrong or are my router's ethernet ports dead?

   It's hard to do anything wrong.

   You might try connecting your (unspecified) laptop to your
(unspecified) desktop.  It may not do anything useful, but if either
side says that the Ethernet physical link is good, then you'll have
verified both Ethernet interfaces and the cable.

   You might try connecting a known-good cable between two LAN Ethernet
ports on the router.  Again, it won't do anything useful, but the
port-status LEDs should indicate a good physical link.

   Visit http://netgear.com/support , put in your model number, and look
for Documentation.  Get the User Manual (at least).  Read.  Look for the
LED descriptions and "Troubleshoot".

   From what you've stated so far, it sounds like a router problem.  But
its wireless stuff works?