...my PC started hard freezing randomly (everything locks up, USB devices lose power, static sound coming from speakers). This would happen randomly whether I was doing anything or not and while infrequent was still a problem.
Ultimately, I managed to get the system to post by removing all of my ram except for one stick. I'm not sure if the problem is fixed but it hasn't happened yet so I'll have to keep monitoring, but one thing to note is that I've tried 2 different sticks in the 2nd ram slot and the computer will not post until I remove it. I haven't tried the ram in the 3 or 4 slot yet but I have a feeling that both sticks can't be bad, so I'm thinking its a fried ram slot. I hope not because that will put me out of commission for a week or two.
Firstly, most RAM sometimes messes up if you put it in the wrong slot. Sometimes it's colour coded, but usually the 1st/3rd are linked, as are the 2nd/4th, and it'll look to the 1st slot initially. Since you have 6 slots, I wonder if it's not the 1st/3rd/5th that are linked, just try them out. I'm sure someone can elaborate better as to why all this is. Another thing to check is that the BIOS is clocking them at the right speed. The RAM's rated at 1600mhz, make sure it's actually running that from the BIOS.
As far as the freezing is concerned, I had the same problem when I first built my PC - I even sent it to a PC repair shop who couldn't figure it out - and eventually I stumbled into what was happening. A lot of mobo's these days have 'green' functions which limits power to devices that aren't actively in use, and some devices - in my case the graphics card - don't exactly take kindly to having it's power yanked off. A BIOS update fixed the problem so it'd be worth trying that.
Sadly, shit like this really COULD be anything. It definitely sounds like a hardware issue though, best suggestion is to unplug anything non-essential; graphics card, sound card, non-OS HDD (even the OS HDD if you can RAID/install an OS to another disk), then plug it all back in one at a time until you know exactly what's causing the issue.