Why do television set have warnings to be careful about touching the circuit components even when the set is turned off?

When power is turned off on any device that uses "more" electricity: E.g.- television sets, computer towers, stereo systems, etc., the circuits, boards, and chips inside still hold an electrical charge. While not enough to cause physical harm or be fatal to your person, they are still very unpleasant to encounter. The equivalent of taking an amped up static shock.

Also, electricity is lazy and always takes the shortest route to ground. If a wire, string, or something that conducts electricity got into your TV and was strewn across your circuit board on the inside, it may be enough to bypass the "On/Off" switch and go straight into you. The shortest route to ground in your body is through your heart. It only takes a couple tenths of an amp of electricity to kill you. Most household electronics can handle and are rated to handle above several amps. In short, your heart will turn to charcoal way before your TV or computer bats an eye.

P.S.- On a less harmful note. Dust inside your computer or television can also be strewn across the fine filaments of the micro-components used to build your TV or computer. These pieces of dust will also provide the shortest route to ground and guide electricity through paths it is not supposed to go and will short circuit your electronic device thus killing it. (Short Circuit or a "short" is the correct term for "frying" your electronic devices.)

P.P.S.- Both these instances are unpleasant at the least, which is why it is highly recommended and instructed that not only do you turn your device off, but you must also: unplug your device from the wall. Once it is unplugged and removed from any electrical source, you must turn your device ON to use up all static electricity in your circuit. (Static meaning electricity that is still and left standing inside your computer or television. "Still" or "Remaining" electricity.) This electricity can sometimes be enough to turn your TV, computer tower, or other device back on for a brief time even though it is not plugged into a outlet. Turning your T.V. on after it is unplugged will use up all the electricity still inside the TV set and will then make it safe to run maintenance on. When all the electricity inside is all used up, your device will lose ALL power and shut down automatically.