Can a microwave cook food if it's not turned on? Does a washing machine clean clothes if there is no power? Will my Tivo record every episode of Eastenders if I don't plug it in (even if I do it wouldn't anyway, that show blows!) ...
My point... if you turn off your PC, unless you have "Wake-on-LAN" and leave the socket turned on nobody's getting near it, wired or not. Going the extra mile and turning off your modem/router, again.. no power.. no signal.. no connection..
If you want to be reallllly safe, pack the whole computer back up in bubble wrap and return it to the store you bought it from.. then, wear a tinfoil hat in case the aliens try steal your credit card details via telekenesis..
Sorry dude, but sounds like "neuron" is short for neurotic.. WPA protect your wireless connection, Don't have any "non-passworded" accounts on your PC and relax a little.. its all good.