Is it new battery time?

A few things wrong here.

Firstly, you cannot "shut the hybrid part and keep on going with just engine". It is not physically possible in a Toyota. The HSD requires the use of both MG's and the ICE. If the engine spins the car can move without it on electric only until the pack is depleted and then your screwed because you will need to grid-charge it.

When you get a code, you need to read it. The check hybrid system code could be anything from a bad battery, to a loose HV isolation plate, to a bad inverter or inverter coolant pump, or loads of other things. There should be sub-codes and exact codes to say what it is.

As your car sits now, it sounds like your gas engine is failing to start and you have depleted the traction battery so it cannot spin the engine enough to start. This is what happens when you drive it to emergency stop on electric only (what you did first), then restart and drive again to emergency stop (what you did before a tow). My guess is now you will need to have the battery grid charged to bring it up enough to start to turn the gas engine on to charge it back up. But you also have something wrong with the engine system. Could be anything as well like a bad fuel pump, clogged coils, who knows. But you have multiple problems right now and without the actual codes, everyone is guessing. The car has told you it was sick for a year, and now it is in the ICU because it wasn't cared for.

 

P0420 is NOT failure in the hybrid system code. That is a catalytic converter failure, or rather below efficiency. This does actually match with what your symptoms are as this is the gas part of the gas-electric hybrid and exactly why when it died, it was the gas engine dying and you drove it dead dead on electric only.

So you have a problem, especially in CA where they test the catalytic converter. It could be the cat, it could also be something like the O2 sensors. But you now also have a second problem completely unrelated to the first that was entirely preventable. Your HV battery is now dangerously low. So low that it won't spin the engine. This means you need to have the battery grid charged. This is much harder than it sounds. Generally dealerships have to fly in specialized equipment to do so. Expect a $1k bill at least for your 200ft of driving when the car told you "no" from the dealership. And then you're back to your actual problem, something wrong with the engine subsystems.

If you know anyone with a Prolong charger and is very handy and good with high voltage DC, you may be able to charge 'er up slowly for free. Or by disassembling the battery and using RC chargers on each module, get it back together. Either way, a huge PITA.

Was it only the P0420 code? Was there shaking before? Rough idles? Smoke? Has someone stolen your cat if you look under the car?

 

Hmm... you got 26K after the light first came on. I'm at only about 15K since check hybrid system light first came on. I guess I can expect another 10K.
Using the OBD2 scanner is so much more convenient to reset the error though.