So you would have no problem trying to "fix" a computer while it's turned on?
I'm not worried that the person would get shocked. More on making more damage on that computer than it already has if it wasn't turned off.
I would have no reason to attempt such. Just stating the facts of the matter- human flesh has a decent bit of resistance...particularly, the dry outer layer of skin. And Ohm's law is, well...law.
Assuming 12v DC, which is obviously a worst case scenario for the voltage level seen outside of a PSU (inside, of course, having some parts getting the obviously-dangerous 110v AC), a human fingertip is not any more likely to provide an alternate path for current flow than, say, the air that is surrounding all the parts. If two closely located traces/contacts/ect are not at risk of arcing through the air and shorting, they're also not at risk of arcing through your fingertips. Not with 12v.
Yes, it WILL take less voltage to arc through said finger than it will the air, but it doesn't change that 12v is simply not enough for either.
Sparks CAN be made with 12v, but it will be as two conductors (i.e. metal) are brought into/away from immediate contact. E.g. plug in a molex connector for a fan while the circuit is live, and you'll see some little arcs. But it won't hurt it. Said arcs are more likely to hurt an actual PCB component with IC's and whatnot on it, but even then, I don't see it. Worst case, you get a burnt contact that needs to be cleaned up.
The real danger (as far as damaged parts) is in something with lots of little connections, like the rows of contacts on an expansion card, where parts that are not supposed to make contact may do such for a brief moment during insertion/removal of the part.
Not saying 'sure, take your PC apart while running'...why would you? That's silly. Again, just stating the facts that answer the OP, since we're a bunch of semantical nerds.