[Coda]

For information's sake: Surge protectors are designed to safeguard against transient power spikes, not lightning strikes. They're rated for a certain amount of power, and a spike beyond that rating will still pass through, and potentially damage the surge protector in the process. A failed surge protector then passes current through unfiltered, so you won't know that there's been a problem.

However, the description of getting an electric shock from your case doesn't sound like a lightning strike or power surge at all. It sounds like, as I said, a ground fault.

Electricity lesson time!
Inside a computer, the electrical components are connected to the metal parts of the case, which itself is connected to the grounding pin of the power outlet (the round third pin, instead of either of the two flat ones), which is then connected to a metal pole in the foundation of the building. This serves multiple purposes, but for this discussion the relevant purpose of this connection is as a safety mechanism: Electricity wants to take the shortest path to the biggest current sink available, and the Earth itself is a gigantic current sink, so this connection takes any excess or incorrectly-wired electricity and provides a short path for it to escape somewhere safe.

A ground fault means that there's live current connected to that grounding somewhere. This could be caused by a failing electronic component, for example, or by a wire connected wrong, or by something metal on a circuit touching the case when it shouldn't, or by water creating a connection somewhere, or by an overheating component melting a little bit, et cetera. If your house wiring is working the way it's SUPPOSED to, a ground fault will cause the circuit breaker to turn off, shutting down power to the malfunctioning device. (In places where a ground fault is particularly likely and particularly dangerous, such as a bathroom where a hair dryer might get wet, the power outlets themselves are equipped with ground-fault interruptors that detect this problem instantly. If the outlet has "test" and "reset" buttons, it has one of these protective devices.)

Unfortunately, a weak ground fault may not be strong enough to cause the circuit breaker to trip, or the grounding connection itself could be damaged (broken third pin on the power cord, for example). When this happens, the metal parts of the device start to build up an electric charge that doesn't have anywhere to go. When you touch it, your own body becomes the connection between that charge build-up and the Earth, so the electricity goes through you -- and you get zapped.