Finding a good way to connect the computer chassis to Ground is a good thing. But there is more.
I don't know the details of electrical outlets in your country, but I'll try to write generally. In many AC wiring systems ONE side of the power supply to the home is grounded to establish a zero-voltage reference point for the system. This is done both at the exterior transformer on the power company's poles, and at the breaker panel in the house. Then cables from the breaker panel to each wall outlet are run, and they are supposed to be installed in a way that ensures the the polarity of the slots in ALL of the outlets is the same. Where I live, it's the LEFT slot of the wall outlet that is always the Grounded Neutral side, and the right slot is "Hot" or "Line". That may or may not have been done when your house wiring was installed.
Still, there is a problem possible. On older designs the two slots of the outlet were the same size, and the two prongs on each plug also are the same size. So it is easy to insert a 2-prong plug on the end of a cord into the wall outlet either way. The problem comes because the user device that you are plugging in may prefer only one way and there is no way for you to know what that is. For a LOT of such situations this does not matter. BUT it DOES matter when you are plugging in many devices and then connecting them together with signal cables. For example, you may plug in separate computer, monitor, printer, and modem, then connect them together. If they all happen to be plugged into wall outlets the same way, there will be no problem. But if ONE of those is plugged in "upside down", it is possible for it to feed a voltage from its chassis to all the other chassis via the Ground shield connections in the data cables.
So, IF the plugs on your devices in your computer system CAN be plugged in both ways ("right-side-up" and "upside-down"), you could have this problem causing the stray voltages on exterior surfaces. What to do?
1. Disconnect that Ground cable you installed. This is only so any stray voltage WILL be detected during this sequence. You can re-connect that Ground later.
2. Unplug all your devices. Disconnect all the cables that connect them together.
3. Plug in only your computer. Start it up and feel its case. If you feel an electrical shock from it, shut it down and unplug, then turn the plug over and plug it in the other way. Start it up again and check for shocks. When it gives you no trouble, leave its plug that way. IF you still get a shock no matter which way it is plugged in, try to pick the way that gives you less shock. Then re-connect the Ground lead you had created, and check whether that eliminates the effect.
4. Now connect your Monitor to the computer and plug it in. Start up both computer and monitor and check for shocks on both devices. If you get a shock, unplug the monitor and turn its plug over, then plug back in. This should eliminate the shock effect.
5. Do the same process with your printer.
6. Do same process with each other peripheral device in your system, one at a time.
This process will ensure that all your connected devices are plugged in with the same polarity, even though the plugs and wall sockets do not appear to have any polarity labels. If you have not yet re-connected your Ground lead, do so now and verify that everything still gives no shock. If this all works, it might be a good idea on EACH plug to mark the "right side" to plug in "up" so you can re-connect properly later if you ever un-plug something.