Sorry for the slow reply - have been traveling. Did you try adding the G.Skill sticks into the black slots, and if so did it boot?
If not, there are two probable conflict areas: voltage and timing. The G.Skills apparently need to be at 1.9V to run properly in dual-channel, while the Patriots only need 1.8V. The G.Skills also have tighter timings (5-5-5-11 vs 6-6-6-18). There's really no way to check what the mobo is trying to default the mixed set to if it won't boot, so you'll need to boot as currently configured (Patriots in white slots, G.Skills not installed), then in BIOS adjust the voltage and then the timing if the voltage adjustment doesn't work by itself. (Running the Patriots at 1.9V won't hurt them.)
First, I would recommend downloading and running CPU-Z if you don't have it on already. (http://www.cpuid.com/softwares/cpu-z.html) Click on the "Memory" tab and make a note of whether the Patriots are running in dual-channel mode (Channels #) and what values are in the DRAM Frequency (this is your real clock freq which should be half of the rated or labeled speeds, or @400MHz in your case), and the first four timing windows (CL through tRAS). These should be showing 6-6-6-18.
Before I get too deep into how to make adjustments, I'll wait to find out if the two sets booted together with the larger sticks in the white slots and the G.Skills in black. If it did, please post the same values I listed above - even if they boot together, they may not be running at full speed.