That sounds like a power supply or heat problem to me.
There can be many possibilities for the problem you are experiencing from an insufficient PSU, to a CPU that needs to be reseated or a HSF that isn't mounted correctly or GPU drivers that are corrupted, DRAM that is malfunctioning and much more. The problem does NOT sound like a CPU issue however. Without knowing all of the specifics of your PC, there isn't much we can tell you other than potential problem areas.
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