Toyota Service Centre Gave Up - Engine Not Running

What is the low power code, P3190?

Basically your ICE isn't able to start but the HV battery was still able to attempt to start it, but it won't 'catch' and keep itself running on it's own. I'm guessing the "rescue charge" means that the HV battery is depleted and won't even attempt to start it anymore.

Essentially it just needs a proper "crank, no start" diagnosis (fuel, air, compression, timing, etc).

The first thing I would do as a complete amateur would be the age ol' 'spray starter fluid into the throttle body' while (or before) trying to start it. If you can get it to stay running a bit like that you know you have a fuel issue. If nothing there I'd check for spark and after that compression. I'm sure I'm missing something, but it shouldn't be that difficult as long as you have a way to charge the battery every few start attempts. You may also have to charge the 12v.

They'll probably be able to figure it out once it gets it's "rescue charge", but if not try to find a real mechanic or a hybrid specialist and if you have to, then build a charger yourself. It's pretty crazy how inept and un-equipped a lot of dealers seem to be.

Edit: the "smell of fuel" would probably change my first action from 'checking for fuel' to 'checking for spark' since that's probably from fuel just not getting burned.

 

I'm assuming the engine doesn't start or even idle. Check for 12Vdc power going into ignition coil - No voltage, no spark, no ignition. Check all your fuses and look over your wiring harness for chew marks and exposed wires.
Open the Air box @ the air filter - leave everything in place. Don't want to suck something into the intake manifold. You can also inject starting fluid there.
How much oil consumption per oil change interval were you experiencing before the motor quit? Have you kept up with factory recommended maintenance intervals? Has the 12VDC battery been checked and verified fully operational?

I would move onto compression test if no other problems are found.