Need opinion , is it 12v battery or inverter

Hello, my wife was driving our 04 Prius when she pulled out from a stop sign into a turn lane when the car stopped. She could only put it in neutral and she said all the warning lights came on. Someone helped push her out of the road into a parking lot. She thinks the ready light was off. She could not turn the car off for several minutes and then she was able to shut it off. When she tried to turn it back on all the warning lights came on and it would not shift into any gear. I showed up a bit later and checked for codes and found none. The warning lights went away. This was I believe the 3rd inverter pump I have installed in around a year. I thought another bad pump so when I got home I checked it but it was running. My daughter had limped the car home several miles once when the last pump went out so my question is could the inverter been damaged during all of these pump failures I have experienced and the inverter is staring to fail because of the overheating?
So I was ready to go get a salvage pump and I thought I would check the 12 volt battery. It settled at 11.3 with lights on. When the pump kicked on 10.8. After setting for a bit and putting it under any stress it would drop below 10 and the red triangle would come on. So now I'm thinking bad 12 volt battery but when the car is running it is normally in the 14 volt range isn't it? Could it still cause a problem when the car is running like my wife experienced?

 

My obd2 reader is a cheap amazon or eBay. Same with my pumps. I now believe if this one fails I should get a genuine Toyota . The battery is in the 4 year range at least. Any recommendations on battery brand?

Now that I think back during the breakdown I had checked the 12v battery with my meter in the back and as mentioned above by JohnPrius3005 I unplugged the larger white cable while I was back there. At the time I had a 12v reading under no load. Now was this before or after I did the code check I don't remember.

I have 256,000+ miles on this 04 model. I also have a 05 with over 271,000 miles. I have reconditioned both traction batteries and been fortunate to get several miles (years) on both. I bought a 3rd used traction battery I keep in the basement as a quick swap out when one of the larger batteries starts to give trouble.

One more thing I just thought of. I had a mouse in the car. I trapped him and he is now gone. Has anyone else had problems with mice getting in the car?

 

The car is running fine now with no codes and goes easily in ready mode like nothing is wrong. I'm going to just go ahead and buy a 12v battery because it didn't take much to start dragging it down. I compared the battery of my 04 Prius to my 05 Prius using the cars battery diagnostic screen and got quiet a difference when putting them under a load. I plan on driving the 04 so I can keep an eye on it and let my wife drive the 05. I appreciate all the help and hopefully I won't be back with this problem. Have a nice day.