I would not worry about any of those codes right now. Figure out the no rpm signal, then go from there. P0113 is iat sensor, more than likely not plugged in, its in the air box. P0475 is for the exhaust butterfly, and p0232 is for the fuel pump, if you have an aftermarket one, it may set the code.
However, these can all be caused by rodent damage, may start by looking at the harness where it passes thru the firewall for damage. I have always gone by the thought of its never the pcm. Whenever i have thought its the pcm, i typically spend another several hours making damn sure i didnt miss something. Rarely is it ever the pcm... Typically it is some sort of damage to the wiring.
Ohm testing works, however, do not use that as a sole indicator that the wire is good. It can pass a continuity check, but not be able to carry any current. Load testing is a much better option. Hook up a headlamp bulb and ground the wire, send voltage down the wire, and measure the voltage drop across the light bulb. It should he equal to battery voltage. If there is any more than a .5v difference, there is hi resistance in the wire.