The wires are safe to touch as they are powered from a 3.3V chip on the motherboard, and current is limited by a resistor.
However, if you carry an electrostatic charge, and you touch the wire, you will cause an electrostatic discharge (ESD). This is harmless for you, but it can zap the integrated circuits at the other end of the wire if they are not protected.
Normally, the manufacturer would have taken appropriate measures to ensure all input/outputs are protected against ESD, which begs the question: did they consider it worthy to protect this particular IO since it is normally not an externally accessible IO, but rather an internal wiring?
For example, looking at this motherboard schematic (pages 23-24), the power button signal is filtered by a 100nF cap which should be fine, however the RESET button signal goes straight to a IC pin without any protection.
While these chips include ESD protection diodes, such diodes are sized to protect against ESD events during fabrication, which are quite limited in charge as people manipulating chips are expected to take proper precautions. More robust protection diodes on every pin would use more silicon area and make the ICs more expensive, while providing no benefit unless the pin is actually accessible on the finished product and can be zapped by the user.
Therefore, your arrangement carries a risk of zapping the motherboard. It will probbaly be safe if the floor is tile and you are wearing cotton. However, if the floor is insulating, and you're wearing wool and sneakers, and the weather is dry, when touching metallic objects your fingertip can turn into a pretty impressive lightning gun!
5Dangerous and electricity depends on a whole host of things. The voltages on those wires should be at most 12V which is classed as a "safe" low voltage. If you simply touch a 12V supply you should be fine. It would be difficult to kill yourself without really trying, but having them exposed and loose could cause them to short against the case, could cause other problems and potentially charge the case up with enough current that if you were earthed somewhere else it could give you a sharp electric shock. It might only "buzz" you, but could harm smaller creatures. Just replace the switch. – Mokubai – 2018-03-06T22:11:45.713
8If a simple "touch" starts the computer, those are not the main power cables, but rather the "on/off" button wires and run on 5V. A chance contact may initiate a computer shutdown, obviously. I'd go for a new switch. – LSerni – 2018-03-06T22:12:08.487
Thanks alot for the answers! (yes it's the "on/off" button wires I'm talking about). Simply getting a new switch button then. – JazzMaster – 2018-03-06T22:22:05.983
41There is no answer to any question beginning with "How much electricity is there in ...". ;-) – Mike Waters – 2018-03-06T23:36:55.767
@Mukubai I don't know how to "charge a case up with current". Besides, I doubt that the voltage to GND is in any way substantially higher than 12 V. – glglgl – 2018-03-07T10:33:37.713
Related: "How much voltage is “dangerous”?" at SE.ElectricalEngineering.
– Nat – 2018-03-07T13:41:53.3371You should also be considering the risks to the machine from you - it's not obvious that the switch connectors have any protection against a discharge of static. – Toby Speight – 2018-03-07T13:57:45.820
A computer I worked on around 20 years ago had two black half-inch thick cables running from the power supply and were fused directly to the front of the case behind the power button. I don't know how much voltage/current they carried, but I sure didn't like the look of the cables or the fact that a user would be pushing their finger right into them to start the computer. – Dave Cousineau – 2018-03-07T18:02:00.583
@DaveCousineau, yes, AT era machines had a big switch for the actual mains input. ATX motherboards have a low-voltage signal to the PSU to switch it on. The mains input is connected all the time, it has to be, for standby power to be available. – ilkkachu – 2018-03-07T21:01:56.590