Codes p0302, p3006, p3000, c1202 and c1259

Keep it and repair it. When I first purchased my 2003, it was almost exactly in the same condition as yours. The previous owner also thought that it was a scrap or parts car.
I am a completely DIY person, and after I gave it a thorough going through of the HV Battery assembly, replacing the cats assembly, and replacing the 12v battery with the proper AGM type battery, I have only less than $1500 invested and the car runs great.

10.7v in your 12v battery is far from the minimum voltage needed to boot up your ECUs and get your car into "Ready" mode to start it. The flickering and fading screen is due to the fact the the 12v battery is below the bare minimum 11.8v to ready the system to start.
After that, it is the HV Battery that actually turns the engine over and starts it, and also charges the 12v battery.

After a good 12v battery sits awhile it should recover to a much higher voltage than that on its own.
Either your new battery is not a good battery, it's the wrong type battery, or you have a draw or a short in the system.
Check the specifications for your car and make sure that you have the correct battery, then charge this battery up to full voltage, get it load tested at your local parts store, to confirm that this battery is good.

Start the car and get all the trouble code readings by using a good scanner that is appropriate for Prius, and get all the voltage reading of all your cells, modules, blocks, from your HV Battery Assembly.

By my own experience I think it is likely that your HV Battery is healthier than you may have the impression it is, and you may very well have a condition that is more related to the functions of the 12v battery system.

I highly recommend that you don't take this to a dealer for diagnostics and repair. They will try to sell you on replacing every expensive component in the system, when in reality, it is all serviceable and restorable for much less, by yourself DIY, or by a good local mechanic who has Prius experience.

Don't write off this car as scrap. If you don't want to deal with this relatively easy diagnosis and repair, then sell it to somebody who is.

 

Looks like battery block 13 is reading low. The HV battery doesn't like it when there is a deviation of more than 1 volt in any of the cells. In fact, it may be less than a 1 volt deviation. I'd certainly take a look there! If that is a "new" HV vbattery (9 months, you said) let's hope there's some kind of warranty to cover this, as that certainly would be cause for replacement.

I replaced the original HV batt. in my '02 with a Dorman, which failed within a year. Fortunately there was warranty coverage for the battery, but not for the labor to install the replacement, so I took a hit on that one. But the second replacement is going strong after seven years and counting.

 

What 12V battery did you buy, and did you check it's voltage before installing it? They sit around between manufacture and sale and lose at least some charge. I always check and frequently put a fresh charge on them before installing. What does the 12V read with the car completely off?

Is this thing running and driving? I see a state of charge on the HV battery of 10%. Then there's the seemingly weak block 13 as Trombone pointed out. Has the thing sat around a lot not being driven? That's the worst thing that you can be done to these batteries. It looks like the HV battery is pretty deeply discharged along with the 12V. Nothing will go right that way. The only thing that keeps me from saying that the HV battery is toast is just that if it gets all charged up maybe some things will get straight...? If it's running and driving - drive it around - a whole bunch. Get the SOC up to at least ... uh, IDK 40%? See about the balance of the blocks is then and what the 12V is doing both off, at initial start up, and while running (in Ready mode).

 

I don't have the most discerning eye among the Prius-knowledgable people here. But those HV battery numbers now look good - within spec.

Keep in mind a few things.
- Drive it, drive it, drive it. Regularly. The batteries don't like sitting.
- Don't be surprised if the HV battery doesn't last long. They're all re-mans using older battery blocks. But your best defense? Drive it!
- Keep a close eye on the 12V voltage. I have a very small parasitic draw (which I've tried a couple of times to find and haven't...) Until (if!) I find that, if it's going to sit for more than like 3 days, I disconnect it. This doesn't help the HV battery - but it keeps me from having problems coming from a weak 12V.

 

Regarding the 12 volt battery, years ago I wired the accessory outlet (f/k/a cigarette lighter) to be "always live" (thanks to a little jumper kit from coastaletech), so now I can boost a weak 12 volt battery by connecting to a 12 volt power source like the Campbell-Hausfeld inflator. This gives enough oomph to boot the hybrid system to "Ready" and I'm good to go.