Ok, cracking this open and getting it up in the clamp. First let's identify the input pin. We know that the yellow wire's job was to bring 12V power to this computer.
So we now know that that pad is hot. That makes sense because look at the thick trace that goes from there up and round to lots of other areas on the board. *Usually* the ground is very close to the hot because in every circuit board I've ever seen, there's some form of capacitor connecting the hot to the ground to filter out noise and to smooth out the power to the circuit. For those of you that don't know, capacitors act like little batteries that get charged and then release the charge when voltage between the hot and ground drops. That ultimately smooths out the voltage over time and is why they are sometimes called "filtering caps" because they filter out noise. One way to double check is to look for marking on the circuit board that identify the ground or hot side of a filtering cap. Sure enough there is one here. (NOTE: This mark on the board is really to document that the capacitor has polarity and that the ground pin for the capacitor must connect to that trace. If there isn't a mark on the board, you can tell which pin is ground because the capacitor will have a white stripe nearest the ground pin of the capacitor. If there is no stripe then the capacitor doesn't have polarity and you'll have to do other tests to figure out which trace is ground on the circuit board.)
So, there is an electrolytic capacitor immediately adjacent to our hot lead. Electrolytic capacitors typically fail at around 20-30 years of age. If you ever see a dead video game console at a thrift store, buy it, replace the one electrolytic capacitor near the battery leads and 9 times out of 10 the machine comes right back to life. I'm willing to bet that is exactly what's going on here. Capacitors fail in one of two ways, either they "ground" or "gap". When they "ground" the hot and ground connect inside and it becomes a direct connection between the two causing a short circuit. When they "gap", the opposite occurs and the capacitor stops working but doesn't cause a short. We know that the hot lead has a direct path to ground so double or nothing, this capacitor has grounded inside. Here's the ground lead on the capacitor on the other side of the board, we know that is ground.
Now let's check to see if the capacitor has grounded inside:
Uh oh. All zeros means that the capacitor has grounded inside and THAT my friends is where the short circuit is. (EDIT: not necessarily, keep reading, the next morning I realized I got ahead of myself with that statement.) After all of that work, it was just a failed electrolytic capacitor. Looking online, this air amplifier unit is a pricey piece of kit. $500-$600. This electrolytic capacitor is $0.25. It's important to note that in *theory* I could just desolder this capacitor and everything would work. If you're stuck in the outback grab a poisonous snake and use its teeth to just nip this bugger right off. That will get you home with A/C and working windows and gauges. This cap just smooths out voltage and it's likely that removing this cap won't add so much noise that the digital parts of this circuit cannot function. I'm not sure though, I've seen computers that are super sensitive to noise and if any one capacitor is missing, it just won't work. I'm willing to bet the boys at 'yota added a little redundancy.
