If you notice that the case gives you a current, something is wrong.
Mount the minimum (motherboard + graphics card + disk + power supply) on top of a wooden table to rule out any contact with the case, which you don't say what it is.
Check that the temperatures are within the "normal" range, that it's not shutting down for safety when it reaches high temperatures.
Out of curiosity, does the outlet where the computer is connected have a ground connection? Sometimes not having it makes you notice that tingling. That you have an outlet with the possibility of having it doesn't mean it's connected... if you could see the mess that's made...
At my partner's house when I touch the faucet and the dishwasher, I act as a ground. And zap. There's something there. What to rule out to start, the ground should always be there so that the current doesn't do its thing. But those CPU temperatures I'd like to see less than 65. In any case, first, as mystique says, rule out leaks because it's the beginning of the end of the chips, circuits, etc.
