If your wall outlets are not grounded then I assume they have only two slots for blades of the plug. Look at those slots carefully. On newer designs one slot is wider (well, taller if they are vertical), and the blades of the plug also are different. If that's what you have, there really should be only one way to plug the plug into the outlet.
HOWEVER, if your plug blades are the same size and the outlet slots are different, you can plug in with the plug turned either way. In that case, unplug, turn the plug over, and plug in the other way. That MIGHT eliminate the shocks.
IF, instead, the outlet slots are the same size AND the plug blades are the same size so that you can plug in either way, try doing that same thing. Unplug, turn the plug over, and plug back in. Again, that MAY solve your issue.
The source of this is that, on any North American outlet, the two slots of the outlet are one Hot and one Neutral. On SOME devices (like you computer) there MAY be a connection to a case part from the power wire in the cord that is supposed to be plugged into the Neutral slot. (There really should not be, but it does happen.) IF the connection at the wall is reversed, the intended Neutral wire into the computer may actually be the Hot wire, and that can give shocks from the case.
There's another related possible cause. With modern outlets that have a round Ground hole, the wiring supplying the outlet is connected in a particular way so that the Hot and Neutral supply lines from the breaker panel are on the correct slots of the outlet. Moreover, with a 3-prong plug you can't plug it in backwards. But with the older two-slot outlets, sometimes which slot is fed from which power wire is not done correctly. In those mistaken cases, even if you plug in correctly, the actual power being fed can be wrong. To detect this error and fix it probably requires an electrician.
If turning the plug over does not solve the problem, then there is another possibility to check. This really would require an electrician to help. There may be a flaw in the way the entire house's power system is Grounded. In North America and many other locales, the Neutral line from the power source is connected to Ground at the transformer AND at the breaker panel. If that Ground connection has failed, then even the Neutral line is no longer at Ground (zero) voltage, and lots of bad things can happen.