I am having issues with my new computer build when running two sticks of RAM. No issues when running one by itself.

Specs:
CPU: AMD Phenom II 550
M/B: Gigabyte GA-MA785GT-UD3H
RAM: 2x2Gb G Skill DDR3 1600Mhz
Video card: Sapphire ATI HD 5770 Vapor-X OC Ed 1Gb
Case: Antec 300
HDD: WD 1.5Tb Green
SSD: Patriot 64Gb
Optical: LiteON IHAS324 24x
PSU: Thermaltake Litepower 700W
CPU Cooler: Cooler Master Hyper TX3
O/S: MS Windows 7 HP 64bit
Wireless: D-Link DWA-510
Sound Card: Createive Sound Blaster X-Fi Xtreme

I put together the above system, and was having issues with artifacting, BSODs on startup, and losing my wireless network card from device manager, hence losing my internet access. I eventually diagnosed that it was because of the RAM – when running memtest86 from a bootable DVD on both sticks of RAM, in any combination of slots, it would cause the computer to reboot about five seconds in to the test. When running with one stick in there, it would work without errors. The BSODs and artifacting also went away.
So, I assumed there was a problem with the 2 sticks of RAM, and I returned them under warranty. I bought a cheap 2Gb stick of RAM to use while waiting for the G Skill RAM to be exchanged.

Yesterday I got the RAM back from being exchanged, and put both sticks in and tried to run memtest86, and the computer reboots within about 5 seconds of the test starting, which is the same result as before I exchanged the RAM.
As before, memtest86 finds no errors when running on one stick by itself, only when I have two in there.

So what do I do now? Resign myself to the fact that I'm only ever going to have 2Gb of RAM in this computer? It seems to me that it might be a problem with the motherboard, and I don't really want to disassemble the PC and wait 2 weeks for that to be exchanged, especially if I don't know if it will fix the problem.

Any help or ideas would be much appreciated!