My board is a gigabyte ga-z68xp-ud3. It's a brand new build. I'm currently breadboarding and it won't boot if any RAM is present at all in Channel A ( the marked channel here: http://i.imgur.com/Zq374.jpg).
Both sticks won't work in Channel A (above) but either or both sticks will work in Channel B, and the system will boot. Is this simply a faulty motherboard?
gaurav_88 is probably right.
trying to get this to work without an RMA, take one module and install it in a slot in channel A. Double/triple checking the module is installed well. Sometimes the module looks like it's clicked into place, but it's actually not.
Using one module at a time, you should be able to isolate the bad socket (very rare to have 2 bad sockets). But if you can get a single stick to work in both sockets on channel A, you have something else going on that needs troubleshooting.