Grounding issues, depending on which area that could be shorted, can have a wide range of issues. It could be so bad that your motherboard or other components could die, or it could cause instability and sudden crashes.
With the issues you have experienced with multiple power supplies (unless you are just one very unlucky person

), it's very likely you have something else going on. Grounding issue, flaky motherboard, bad video card, etc.
Now you need to start the process to figure it out. By bench testing it, you will be ruling out a grounding issue with your case. Additionally, when you begin testing it, you can select to use your CPU's integrated graphics in the BIOS, and remove your video card. That way you can test and see if your core components (motherboard, CPU, RAM, hard drive) are good. If so, you add back in the video card and see if the issue begins again. If not, you install it back into the case, triple checking you don't have a rogue stand-off somewhere touching the part of the motherboard (outside of the correct mounting holes, of course).
Each one of those steps should help you identify if there is a problem. If it is truly another bad power supply, you should experience issues with just your core components (listed above), or especially when you add back in your video card and put a load on it (game or a benchmark utility).
Since you said you have already tried multiple PSUs, and still have the same issues, that's why I put it at the bottom of my mental checklist on what your issue is.