I agree with Leon...if it is consistent when you close the case door = short. A very weird and hard to envision short. Hence why he would like to know what case you have...plastic door? All metal? ....
Was your case bent in shipment? I could see a closed door flexing the case so perhaps the back of a motherboard was shorting out to the case. Or pushing on something that results in a short, but generally the case would have to be crowded.
I hate to say this reminds me of a joke but the punchline modified would be, "So don't close the case."
edit -- I guess I would pull all the wiring, and reseat it. Pull and reseat the memory, and double check to make sure it reseated properly (DDR2 can be a pain). . And as Leon suggested put only one stick back and see if it boots. I would check the backplane to make sure none of the tabs is poking into the USB or other ports and appeared properly grounded. I would inspect behind my motherboard to make sure there were no groundings and all the proper standoffs were installed.
I suppose if the door is pressing on wiring that has a break altering the response of a broke wire when it gets flexed. You may want to inspect, replace cables... or move and bundle them if the door would have anything to do with them.
I would also pull the second GPU until I had a working stable system and then put it back.
If that doesn't work: Try to remove as many variables as possible, and with a minimum system see if it boots. I would have downloaded all the most recent drivers (and non-beta BIOS if stable) and make sure they are up to date (I am actually only concerned about when you get to the new GPU, but the rest won't hurt.) If yes, start adding things back one at a time. I guess along the way close the case door. A pain, but it is the symptom. Hopefully at some point it will misbehave, or you will have worked it out.
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