Grumpy_Mike:
Be more specific, in what way is it not grounded correctly?
If somewhere in the electrical installation, someone swapped ground and neutral (it happens!) then you run into freak accidents where the appliance tries to pull current trough PE (protective earth) and that will give the issue that OP is having.
Earth fault (swapped wires) or wrong potentials on PC but correct grounding on the power supply.
Suddenly the ground connection on the external PSU is better than the one the PC has, and current will go that way - leading to hot wires.
Not long ago, my friend was working on some interactive art installations at a tram station and they had electrical issues in the art exhibit gallery room - called the electrician and he found 16 square mm ground cable melted and still hot, and NO fuses blowing - called the tram contractor and they looked more into it, shows the grounding for the tram system was failing so current found a "shorter" path to ground trough that electrical box.