Battery problems despite replacing 12V Battery

Your post is confusing. Do you have an SKS vehicle or the kind where you have to put the fob in the slot? I'm asking because some of what you describe is consistent with a dead (or nearly so) key fob battery. If you open the door with the physical key in the fob, then put the fob in the dash, then turn on the car, does it start?

That said, you might also have a defective 12V battery or some related problem. Find somebody who owns a voltmeter and check the voltage on the 12V battery. It should be well above 12V, on a fully charged battery something like 12.7 or 12.8 volts. Preferably right on its posts, but under the hood between the jump point and a nearby ground (one of the bolts on the inverter will work) won't be very different. The 12V batteries in these cars are easily destroyed by certain driving patterns (few short drives each week, they died in droves during the pandemic) or by one or more deep discharges (a broken door sensor would do this pretty quickly, drawing about 500 mA continuously when off inside of the usual 25 mA). Defective 12V batteries are also a thing, that is batteries that are DOA or fail shortly after installation.

Once the car is running have somebody check it for codes. Not all code readers can see all Prius codes. Not sure if the ones at Autozone and the like are up to this task.

It is possible for the 12V to be so bad that it will not start the car immediately after it is turned off, but that would be pretty unusual. Once a Prius has started it will run with the 12V detached (don't try it, but others have). While it is running the 12V will be charging, and while it takes quite a while to fully charge it, it doesn't take very long to push enough charge into it so that it can start the car.

 

take the battery to an auto parts store for a fre load test. sounds like it's shot.

it should be under warranty, where did you buy it?

 

You may have gotten a bad new battery and/or you have a parasitic drain on the battery.
1. bad new battery: They're heavy and lazy minimum wage workers tend to "toss" things around. That's how you get a new bad battery.

2. Parasitic drain; rust, heat, and moisture can cause alternative pathways to ground. This causes a slow or rapid discharge of a new battery. You'll need to track down the discharge pathway.

Hope this helps.....

 

Or just poor connections at the 12v battery (+) or (-) terminals or (-) cable connection to car body.
Perhaps the main 12v cable isn't fully seated into the quick connect socket at the (+) terminal.
Check all that just in case you have a potential easy win. If no solution, definitely have battery checked.
There have been instances of batteries being drained by small lights that stay on or other small loads that are stuck on, like a washer fluid pump. Finding a parasitic load like that takes a bit of troubleshooting.
When the car acts dead, are you able to use the mechanical key to open the door?
Have you tried inserting the FOB into the dash slot? If so, does the car recognize it?
Does the little red light in the upper right corner of the FOB light up when you press any button? Maybe weak FOB battery?