Static electricity when touching any metal after power down
You have more than 63v AC on GND. But that could be just a few uA of current, so it's still safe and some sort of normal, if it works. In your case it doesn't work because the radio (and audio) is a sensitive application; it requires a perfect power source, free of noise.

In some cases such AC leakage can burn some of the components you have connected anywere on the gnd line (ex: some usb devices).

The best thing you can do is to power your circuit from the PC ATX PSU using one of its spare molex connectors. If 5v are enough you can use the red wire 5v, if you need 6v you can use the yellow wire and a DC-DC buck converter to lower the voltage from 12v to 6v.

This bypasses the need to pay attention to ripple, differential noise, CM noise, and so on, that come from the crappy powerbar+PSUs you are using. And make a complex filter for it. Plus: you get rid of fear to burn some peripherial in the long run.

If your ATX PSU is a good one, it will have all the filters already in place. But you could get some noise on your cables and the new DC-DC converter. So, in any case placing a couple of caps (uF elettrolitic + pF ceramic) on the power wires, as closer as possible to your external circuit, will reduce the noise enough to make your radio work. If you have an oscilloscope hook the power line up and make some tests with different cap values to see which combo gives you a better noise figure. You can use also more than 2 caps; the key is to use different sized caps, and different tech ones (electrolitic, ceramic, mylar, and so on).

This is the easy going approach. Isn't the best, but probably the one that can give you a working thing in the shortest time. The proper approach is to have specs, know the equations, and do the math to build the exact filter you need. But usually you don't have the specs, don't know the equations, and building the proper filter requires expensive/exotic components that usually are not readily available around you. A couple of simple caps instead are all around you: just desolder some from a broken piece of equipment you trashed in your basement, and you can keep going.