Don't worry about damage to your computer, worry about damage to yourself!
Are these static shocks or shocks from stray mains voltage? If it is the latter, then you really need to take this seriously because it could cause bodily injury.
Can you tell the difference between a static shock and a shock from the mains? Do you have access to a voltmeter? Does the shock only occur the first time you touch your equipment after sitting down, or does it occur any time you touch it, even after having touched it several times before and doing nothing in the intervening time period? Is there a spark or a snap when you touch the equipment, or more of a buzz? Does the sensation persist while you are in contact with the equipment, or does it last but an instant?
Note: I'm not asking you to experiment, I'm asking what you have already observed.