Looks like electrical inteference. It *could* be the PSU, but if you have a junk PSU -- and it sounds like you do -- it shouldn't ever be running a GPU that requires supplementary power. So, replacing the PSU with something safe and reputable is an obvious first thing to try, given that it should have already been done under any and all circumstances.
There are other things to try. There could be an issue at the house, or with something else plugged into the same circuit as the PC (I'd only have the PC and monitor plugged in to that circuit while testing). There could be another device or an electric fan nearby. Knowing the history of the problem and this PC would be far more useful than just knowing that the problem exists. The more specific and detailed you can be, the better the chance that we can remotely lock onto the primary problem.