Honestly, I'm more concerned about the general lag after a few minutes than the kernel-power error. I honestly believe that the power issue is a symptom just like the lagging, but even if it is unrelated it is the less severe issue. I'm also pretty sure I'm pushing more than enough power for the build.
Here is the build:
Intel Core i5-4670, Gigabyte Radeon R7 260X, NZXT Source 220 - System Build - PCPartPicker
CPU: Intel Core i5-4670 3.4GHz Quad-Core Processor
Motherboard: Gigabyte GA-H97M-D3H Micro ATX LGA1150
Memory: Corsair Vengeance 8GB (2 x 4GB) DDR3-1600
OS Drive: Sandisk Solid State Drive 128GB 2.5" Solid State Drive
Storage Drive: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive
Video Card: Gigabyte Radeon R7 260X 2GB WINDFORCE
Case: NZXT Source 220 ATX Mid Tower Case
Power Supply: EVGA 500W 80+ Certified ATX Power Supply
One thing I haven't done is run the comp straight off the MB/CPU for video to test if the video card is overheating or malfunctioning. That is my next step. Are there any good ways to test for CPU or MB issues?