Thanks for your input guys. I'm sorry I couldn't post before, but without my computer it's harder to get internet access.
I've done some more tests. As instructed by Corsair Support, I tested each one of my memory modules with memtest86 (from a bootable CD). The first time I started the test, memtest froze on me; the screen just turned green/blue:
I turned off my computer, turned it back on, and re-ran the test. It did three passes successfully without errors. I then swapped the memory module for the other one (in the same slot) and did the test again. The second module also went through three passes with no errors. I emailed my results back to Corsair, but I guess they'll reply monday.
Now, I've noticed a regular behaviour in the errors. The computer seems to be much more unstable (POSTing problems, BSODs in Windows) when I'm using BOTH memory modules. I've even had BIOS lockups and lockups immediately after POST:
(notice the weird dot patterns)
I've tried putting the memory modules in different slots, but it's all the same. This seems to be pointing out to a motherboard fault, either with the slots or the memory controller, wouldn't you agree?
With one stick (which module doesn't make a difference it seems) I can boot into Windows 9 times out of 10, but it's not 100% stable (I got a couple of BSODs yesterday when trying out Battlefield 2).
About a possible hard drive issue, thanks for the suggestion but I don't think that's it. I've run a full surface scan already, and it's clean. More importantly, I've had POSTing problems with no hard drive at all.
So I'm increasingly convinced it's the motherboard that's failing. However I don't want to RMA it until I'm sure all other components are good. The CPU could still be the cause, since I don't have any means to test it. I don't think so, but it's possible.