I know that the answer is yes, I should, but outlets near the setup are not grounded (even though they look like they are) and I don’t want to have wires running though my living room.
The real question is what are potential problems ? Occasional system reboots? Permanent damage to PSU? Permanent damage to other components?
Permanent damage to PSU? Permanent damage to other components?
Or worst: permanent damage to yourself.
I mean it depends on the intensity of the surge, but basically you’d be making it so your PSU is unable to protect the devices from surges. The more sensitive the electronics, the more critical the ground is and CPUs are pretty darned sensitive among other things. And depending on the type of components in the PSU, “surges” also include things like inrush current. Basically, when you turn on a transformer or certain other devices, there is a surge of sometimes as much as 10 times the rated current to create the initial magnetic flux. Depending on the components, this excess energy may end up getting shunted to the ground to avoid pushing it through your electronics. So if it can’t do that, you likely will blow fuses a lot when switching the power on (hopefully there are fuses), or if you’re touching the case which is supposed to be grounded, you may end up getting that jolt.
Anyway, without grounded outlets, and especially if your electronics are cheaply made because many expect there to be grounding and don’t build in extra components to deal with not having a ground, you are likely to significantly reduce the life of your electronics, your life, or start a fire without even considering major surges. If you have a high-end PSU, you may never have a problem until that surge happens. How stable is your power? Because even a normally small surge combined with a cheap PSU, and no ground, is pretty likely to end up in damage to electronics at the best case.
You don’t need to have wired across the room. You can put them through the wall like every other cable. If the wire tubes are not full, it isn’t very complicated. I put my Ethernet wires in the wall.
Run the ground into the ground. You can get metal wire that would work nicely.
Except in very rare configurations (i.e. not 99.9% of residential), you do not want to have multiple paths to ground within a system. All grounds should go to the tied ground/neutral bus in the main breaker panel, which then goes to earth via a ground rod or a clamp to a copper gas/water line, etc. Otherwise you can have current flowing in ways that the system isn’t designed for, which at the least can trip breakers and GFCIs, and at worst exceed the rating of the wires in a short condition and cause a fire.
Except in very rare configurations (i.e. not 99.9% of residential), you do not want to have multiple paths to ground within a system. All grounds should go to the tied ground/neutral bus in the main breaker panel, which then goes to earth via a ground rod or a clamp to a copper gas/water line, etc. Otherwise you can have current flowing in ways that the system isn’t designed for, which at the least can trip breakers and GFCIs, and at worst exceed the rating of the wires in a short condition and cause a fire.
Without a ground there is nowhere for a surge to go, permanent damage is much more likely. Surge protectors or a UPS will not protect against surges at all without a ground.
There’s also no ground so the chassis may have enough voltage on it to cause a shock if you touch it. This could also damage components as they are not grounded and touching things can introduce high voltage from static electricity which will have nowhere to go.
Additionally if you have ethernet connected to it the system may end up grounding itself through the ethernet cable, if the device at the other side does have a ground, which could cause issues.
So it basically just means you have a much higher chance of damaging the parts, or injuring someone touching things.