That would be the exact opposite of what you should do. What you did was insulate the case from ground and any voltage potential was remain ungrounded.
It sounds like you don't have a ground at your power source. Do you have a three prong plug? Is your supply 220V?
You should have three wires coming to your case. One is hot and one neutral for 120V and the third would be ground.
For 220V you would have two hot wires and one ground.
If you have a three prong plug coming from your power source try a new one. If the third wire (ground) is not complete, or open, then the case is not grounded and that is where you are getting the potential to ground from.
If you try a new cord/wire assembly and you still get the shock then your receptacle is not grounded.
Is it your house or are you renting? If the receptacle is not grounded then you will either need to plug it into a grounded receptacle or have that one grounded. If none of that is possible perhaps you could tie the PC case to a ground such as a water pipe.
Is the PC a name brand such as Dell or is it homemade? Another slight possibility is that the power supply itself is not tied to the case with screws but that would only be possible if it's a homemade job.
Let me know what you find.
Thank you very much for your extremely helpful information, I will get working on it straight away. You are right the plugs are all two prong so it isn’t grounded (or “earthed”). The machine is an Acer so it shouldn’t be a production problem.
Thanks again.