Question about 'Check hybrid system'

This morning on my way to work I got the orange triangle of death and a "check hybrid system" message. I pulled over to the side of the road just in time for the acceleration to die. It wouldn't let me accelerate at all; I couldn't even creep along at 2mph. No response to the gas pedal whatsoever, and the engine wouldn't turn on, it was running in battery mode. I turned it off and back on and was able to limp home after the restart. The three codes I have are P0A80 (archive/permanent/inactive), POAOF (engine failed to start), And P261B. This makes me think that the issue is my water pump failing rather than my hybrid battery failing. I just ordered a water pump and will replace it to see. But I was hoping someone else might have advice, or have info from experiencing the same thing themselves. I have the Dr. Prius app and three of my battery modules are low. Getting the three individual modules would cost $900 here where I live. So if the issue is the battery rather than the water pump, I wonder if anyone has advice on the cheapest way to fix or replace the battery.
Thanks for any help!

 

Thank you for your reply! The puzzling thing is that it happened within 5 minutes of starting the car on a cold morning with not much acceleration--just cruising at 50mph on a flat road. I wonder if the engine could get to 220f in those conditions.
The car has 170,000 miles and is a Gen 3 with a Gen 4 engine, which I had installed 4 years ago after I realized I had a blown head gasket. I had a vague memory that they replaced the water pump when they changed the engine, but I may be misremembering.
I ordered an Aisin water pump from Amazon for $130.
Thank you for pasting Chapman's below. It's encouraging that changing the water pump may do the trick. When I first saw "check hybrid system" I thought the battery must be going. I do have a PAO8O code but it's an old inactive one

 

Thank you. I did buy an Aisin one and am glad they're known to be good.
I appreciate your help; you helped me out with useful info when I first bought this Prius and was having some issues four years ago! Since then it has been running great.