I feel your pain, i have had the EXACT same problems as you. I am fairly convinced that it is due to RAM incompatibility, but that doesn't help me at all.
I RMA'ed my DQ6 and E6600 to where i bought it from, they tested it and said both worked fine so returned them to me (only after i paid £35 in charges though!
)
I went on to the assumption that it had to be PSU related, since this problem persisted even when the CPU was the only thing hooked up to the motherboard. I replaced my Enermax Noisetaker 600 watt PSU with a HiperPower R-series 580 watt. I went with this PSU because i read it among the specs of a test system in an E6600 review. The only difference this had was that the motherboard would now give me the rapid beeps when there was no RAM installed.
So i then went with the assumption it was RAM related. My 2gb OCZ PC2-5400 Gold dual channel kit was returned and i bought a 2gb G.Skill NS series PC6400 kit. I chose this because this RAM is sold as being for Intel systems only, so i figured it had to be compatible.... WRONG! Same problem. That was when i finally (completely by accident) stumbled across the Gigabyte P965 RAM compatibility thread in this forum.
For Giagbyte to release their 965P series boards in this state, with so many incompatibilities with RAM, is a joke. I have spent almost 3 weeks trying to get my PC to work. My simple CPU, motherboard and RAM upgrade turned into a CPU, motherboard, RAM, power supply and RAM again upgrade and it is STILL not working. Add the fees for having my RMA'ed processor and motherboard returned, plus fees for having 2 local PC repairmen coming to have a look at the thing since i was completely stumped and it ends up with me being extremely ****** off, way more out of pocket than i should be, and my online business in tatters because my main PC has been out of action for so long and i have no way of accessing my work.
NOT happy at all....