Random Crashes on Homebuilt PC

I built my current computer two years to the day two weeks from now, and I've never had any issues with it other than some bad memory when I first built it. I recently bought new memory for it because I felt four gigs just wasn't enough anymore. Less than a week later I started having issues with my computer crashing randomly while playing games, and the memory is the only piece of hardware that has changed.

The first two crashes I had my computer just lost visuals completely. No BSOD, no lines or anything. My monitor just simply said "No Signal" and I no longer had sound or visual. The computer itself sounded as if it were running normally.

The second crash was similar, but this time my video card fan began blowing at full speed, something it almost never does. So I thought ok, it's overheating. I gave my system a good cleaning, checked all of the fans, and attempted to induce a crash to test the temperatures.

Instead of the same crashes I was experiencing they've changed. Now when it crashes I keep visuals, it just freezes and I get a loud, rapid clicking noise. There is no error report accompanying this. I experienced this two more times while monitoring CPU temperatures and they never reached above 42 C. This current error is similar to what was happening when I first built my computer and was having memory issues, so I ran Memtest, and everything passed with no errors. I then stress-tested my graphics card, which is the only component I can think would be doing this other than the RAM and the CPU, and, while it hit up to 85 C without the fan increasing past 40%, is still technically in the safe-zone. There was no crashing after an hour of stress-testing, and I am at a loss.

Any ideas on what it could be and what else I can do to test this or what component could be causing crashes like these? As much as I would like to just replace this computer I can't afford more than one or two large components at the moment, and I'd like to fix this issue as soon as possible.

This issue happens regardless of what game I happen to be playing, as long as it is somewhat system-intensive.