Diagnosing random black screen crash

Earlier this week I moved my computer into a new case, added a new hard drive, and switched from running Windows 8.1 on a regular Hard Drive to Windows 10 on a Solid State Drive. The inteals of the computer (Motherboard, GPU, etc.) are otherwise unchanged.

Since then, my computer will occasionally totally crash. When it crashes, both of my monitors (which are connected to the GPU) will suddenly go black. Sometimes an audio clip that was already playing will continue (Such as a song in Spotify). The NumLock indicator on the keyboard stays lit, although pressing the key doesn't toggle it. The fans on the motherboard and GPU continue running as well, which leads me to believe the computer is still on.

Once crashed, the system does not recover. I have waited five minutes and it remains in this state unable to do anything. There is no waing before the crash occurs, and there's no consistent patte - Sometimes the computer is up for multiple hours, sometimes only twenty minutes. Sometimes I'm just browsing the inteet, other times I'm playing a GPU intensive game.

I'd like assistance in either solving the problem or at least tips for narrowing down which component is causing the issue. Here's what I've tried so far:

• I've run Furmark and prime95 for 10 minutes each (both separately and simultaneously) to ensure it wasn't the GPU or the CPU causing the problem.
• I've replaced the Power Supply Unit with a higher wattage one.

In case it helps, here are the parts involved:

• Processor: Intel Core i5-3570K CPU @ 3.40GHz
• GPU: AMD Radeon 7950
• Power Unit: Corsair CX750M
• RAM: 2x 4GB Corsair CMZ8GX3M2A1600C9R
• Motherboard: GIGABYTE GA-Z77N-WIFI 1155 MITX

I'd love a solution, but I'd settle for tips on figuring out what exactly is breaking, since the crashes seem random

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