First, you should unplug your computer before you work on it. It should not be relevant at this point if you have a true ground in your house. In a perfect world, everything you assume grounded would all be the same. Have you tested your outlet and compared it to the plumbing? I don't even know from what country these posts are coming and how their building codes are written (or followed). However, you should be save if you are in contact with the case/PSU.
Also, what we are saying here applies only to the low voltage work in your computer. You shouldn't open your PSU or monitor unless you know what you are doing or are feeling suicidal. If you do have to open either, DON'T ground yourself to anythying!