So...whatever the problem is it's ruined three ECU's? That doesn't sound like a bad ground but rather an electrical short of some kind. I've heard about resetting ECU's by disconnecting the battery for a half hour or so but seem's you're accomplishing the same thing by removing and swapping them between cars. Maybe, maybe not?? Have you thought about a possible short in the ignition switch? I supposed a bad ECU would rule out any reliable OBD codes but maybe give it a try?

I agree with Machine Man's analysis. The key for me was the statement "it would start as you let off the ignition switch". With the starter motor engaged, voltage on a stress system is reduced, and when you let off, the voltage rises enough to get it to catch. I've seen similer on several other cars over the years. The recommendations to check the grounds are excellent, both at the battery and at the connection to the body and engine as well as other various key components. I had a friend replace the starter twice. I kept telling him to check the ground, he did, but at the battery only. The corrosion was underneath the fitting where it mounted to the body. Good Luck!

Jerry
01 V70 T5

Sounds like very low voltage from the battery. Bad ground cable from the battery or low charge/aged battery. Grounds are very important. Cranking voltage should never fall below nine volts. Make sure you have a good battery and grounds to frame and the engine block. I start out taking a digital voltmeter and putting one lead on negative lead of the battery (cables connected) and the other lead to the best metal ground on the engine and then the frame. You want to see the lowest 0.01 volt to 0.02 volt you can get. Any thing above this means less than a perfect ground. Cables can have corrosion under the insulation. Copper should look like copper. Not black colored or blue powder anywhere.

Most of the electronics operate on five volts and very low current draws. Connections of all types have to be clean and bright. The more new looking the better! I use electronic control cleaner on injector clips and simliar connectors. Just taking them off and on scrubs the surfaces that can temporary make things better! All these things have to communicate. At 5 volts its like smoke signals. Tarnish is like having fog!