I had similar Gateway PC with similar problem dumped by my wife's cousin who left for college. First time it was HDD, so I replaced it. Then it was Video card, so replaced. Then finally, I figured out it was PSU, then dumped it to a local recycle center, after pulling off CPU, memory, HDD, ODD, etc., some of which were sold on ebay.
Anyhow, to identify root cause, you need to have a working PC on hand so that you can swap components until isolate a real culprit. Then you can replace the component, or like I did, sell all other healthy components on ebay, and build a new system.