I bought an '03 Prius with a bad traction battery. I replaced it with a remanufactured one from Dorman and the car would not go to "ready". Scanned for engine code and got 1636. Called the tech help line and was told the battery control module is not communicating with the ECM. He sent a schematic and I checked the ECM and found no voltage on the comm. lines. I also checked at the battery and got nothing. They sent another battery out on warranty and I still have the same issue. They told me that I probably need to take it to the dealer. There are 235K miles on the car and it was well maintained. I've been told that the non prius compatible scanner will give incorrect codes.
BTW, the 12V battery is reading about 12.2 with no load and pulls down to 11.5 when turned to start. The voltage won't go any higher, even with a running Tundra hooked to it with jumper cables.
Disconnect the battery and charge it with a charger. You can watch the dc voltage with a cheap multimeter, Harbor Freight gives them away with coupons. If your battery tops out at 12.2 v, you need a new battery. And that would keep it from starting (don't ask me how I know.)
Quick way to check if the 12v battery is the problem is to "jump" start it. Just hook jumper cables to another car and start the prius.
Did someone properly diagnose the car before ordering the battery? Maybe there was something else wrong with the car before? i.e. did the car ever READY up and/or did you see the engine run for more than 10 seconds? I've seen lots of armchair mechanics jump to conclusions without a proper diagnostic first. I suggest you get someone with Techstream to do a complete diagnostic. Also, are you sure the key you have is paired with the car? i.e. when you insert the key into ignition does the security light go out immediately?