This is potentially very dangerous because electricity is leaking, and you need to stop using the computer right now until it's been repaired. I am serious.
I suspect that your computer is not plugged into a grounded 3-prong outlet because if it were, the leakage would go to ground, and you would not feel anything. But some homes have 3-prong outlets that aren't really grounded, and a 2-wire cord will nullify any ground connection.
Very likely a high voltage component inside the power supply is touching the metal case, but other possibilities are the wiring for the power switch of any AT supply (but not an ATX supply - no high voltage goes through its switch wiring) or a transformer inside the supply. Or the problem may lie in the power supply of one of the other peripherals, including the monitor or monitor. Regardless, your problem must be diagnosed properly, but I would not have faith in the typical computer tech because most aren't very familiar with electricity. A better bet would be a tech who specializes in video monitors or TVs.
You or the tech needs to measure the AC and DC voltages between the chassis and earth ground, but a low voltage reading does not necessarily mean all is well. Readings should be taken with the computer system and all its peripherals hooked up and also with the peripherals disconnected and unplugged.
Very likely you need a new power supply.