Upgrade or Scrap and start new?

Should I scrap & start new or update?

Last year, I purchased a built computer (big mistake) and it consistently has blue screen of death issues (generic - Check Exception, or something). I took it in to a local shop, and he thought I didn't have a strong enough power supply since ram/hard drive/ etc. tested okay. After upgrading that - same problem.

I didn't find the right solution

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