Loss of Acceleration and Battery Code

I have a 2005 Prius with the original battery. One day, the scary triangle came on. Nothing happened right away, but later as I was driving it, the car started to loose acceleration and the hybrid battery intake fan went on high speed. I cut the car off for about an hour, and started to drive it, but the car loss acceleration again. But when I tried driving it again, I rolled all the windows down. Lots of cold air came into the car and the car drove just fine. However, the engine didn't stall anymore, but kept running even while the car was idled. I imagined the additional cold air coming into the fan kept the battery from overheating.

I did have two codes that came on. One is P0A80 (replace hybrid battery) and the other is P3013 (battery block 3 becomes weak). Here is what I don't understand: why would a failing battery cause the car to lose acceleration? Why would a failing battery cause the battery to overheat? I'm wondering if the codes are accurate or are they false readings.

Here is what I have done since getting those codes:

• I've cleaned out the hybrid battery fan.
• I've replaced the 12 volt battery.

After making the changes, the car started running fine and the engine would finally shut off when the car idled. Obviously, it's because I've disconnected the 12 volt, and thus erasing the codes. But then the red triangle came back on after driving for maybe 10 or 15 minutes and the engine no longer cuts off. It also looks like that the battery isn't holding a charge anymore. The car drives fine, but I don't drive it long distance just in case it loses acceleration again.

The only dashboard lights that come on are: red triangle, the circle with the exclamation mark, and the "check engine" sign. No other lights come on.

I did check the inverter water pump. The pump looks like the original. I do see some fluid movement in the coolant reservoir of the inverter, but I don't know how violent the movement should be. There looks like slight movement. Could it be the pump, though? I didn't get any codes for the inverter.

If it's the battery cells of block 3, I'm prepared to change them out. But I don't want to do that if there is another problem that is throwing a false reading.

Thank you for you help!