Unfortunately Mitchell (my tech info provider) has been down all day so no way to check any diagrams. The ground wire being disconnected killing the engine simply means you have located the ground point for the PCM or other necessary items like the injectors. If it runs with it connected it is fine.

The ignition switch issue is there are several circuits running through it. One circuit powers the PCM and engine running items and another powers the trans, among other things. IIRC, the AC/heater blower motor is on the same circuit so it is common to get glazed switch contacts on that one from the heavy load. Engine starts and runs fine but no power to trans, throws codes, but not every time in the beginning as sometimes it makes good contact, others not so much. This is where the home-made headlight bulb test light comes in handy, if the pink/E terminal wire down on the trans can light the headlight bulb brightly, the ignition switch is providing enough power. If it won't light or only dimly, then likely the switch contacts are glazed/burnt and not passing full amperage. Need a helper cycling the switch a dozen times or so to eliminate the possibility the one time you tested it was the time it made good contact.

A multimeter can read 12 volts on the circuit because it draws essentially no power to get a reading, add a multi-amp load and bad contacts can drop to near zero volts. A traditional test light is also a very low power draw. Think of it as a garden hose with the faucet just barely cracked open. Open the nozzle a little, it sprays just fine. Open it all the way and you get a trickle of water out.

The intermittent problems are the hardest to diagnose because if the problem isn't active when you do the tests, of course they are going to pass! A single solenoid electrical code is most likely a bad solenoid, multiple codes are likely a wiring or power issue. Basically, you turn on the ignition and 12 volts is provided to the E terminal at the trans. Inside, that wire branches off to all the shift and torque converter clutch solenoids to power them. Each solenoid has a ground wire that goes to the PCM. When the PCM wants to turn on a particular solenoid it grounds the wire for that solenoid. As part of it's self diagnostics, the PCM looks for 12 volts on each solenoid ground wire as a check for a good circuit. If that voltage is not present or lower than normal, it throws the solenoid code specific to that one.

If only one code is thrown, we can safely assume power is getting to terminal E because the others are not triggering a code. If all the solenoids are throwing a code at the same time, the first suspect is no power at terminal E as that would account for no voltage at any solenoid wire to the PCM. If good power is at terminal E (verified with the heavy load of a headlight bulb) but it still throws multiple solenoid codes, the next best suspect is the wiring harness between the trans and PCM. Rubbing against a sharp edge, exposing/cutting the wires, or more commonly it is routed against an exhaust manifold or pipe and melts.

We have also seen a major increase in rodent damage to wiring, at some point most manufacturers went to a corn or soy oil based insulation plastic instead of dinosaur oil and apparently the resulting product still has a residual taste or smell of the parent product. Squirrels and mice love the stuff! Even older Dino oil wires suffer because they have chowed down on the newer wiring and give the similar looking older stuff a try even if it has no taste/smell that they like. A careful visual inspection of every part of the harness you can see is a good idea when electrical gremlins appear.

If no codes are being triggered at the moment, try wiggling/shaking/jerking the wire harnesses, many times a wire breaks inside the insulation and is held together end to end good enough to work until a bump is hit just right and they shift apart. Or the damage is hidden on the back side where you can't see it, moving the harness might make the bare wire touch the engine/rans and ground it out.

There are a couple failure modes of the wires that would cause the no power at the PCM end of the solenoid wire. First is the broken wire/open circuit. This what we are testing for when you jumper the E terminal to A, B, etc. to send power up the harness to the PCM connector. If the headlight bulb doesn't light when connected to battery ground and the wire you are testing at the PCM connector, you have an open circuit.

Second is the short to ground. When you attach the jumper wire to power a particular wire, since the other end is hanging in mid air nothing should draw power or cause it to spark. If putting the power wire E to say terminal B produces a spark and blows the fuse, you obviously have a short to ground, likely because the wire touched the metal parts of the vehicle and wore through the insulation or they melted against the exhaust. This has the effect of turning on the solenoid all the time.

A third failure mode of the wires is a short to power, in which case power will be present at the wire even if the E terminal is not jumpered to it. Rare, but does happen. Most often when the wires melt together.

As you have already discovered, just throwing new parts at a problem can get expensive quick! Proper diagnosing is essential, especially with electrical issues, and it takes time. A common complaint is a repair bill will charge a hundred bucks or more labor, and the only parts will be a few bucks for crimp connectors and tape. "Why did installing a couple crimp connectors cost so much?" Because it took me 3 hours to track down the broken wire inside the harness!

I would start with load testing terminal E at the trans connector using a headlight bulb. Again, cycle the key several times to make sure an intermittent issue shows up. If it works every time it's probably a damaged external harness.