2007 Prius won't light up

11.something under load is normal. There is a pretty substantial current draw, and any battery's voltage will decrease more the greater the current outflow. In our car if the start button is pressed once without a foot on the brake the voltmeter will show a number somewhere in the high eleven range, like 11.7 volts. And that isn't even really starting up the car fully. <10 under load is voltage collapse, in this or especially an ICE vehicle with a starter. Between 10 and 11 is a bit of a grey zone, the car might or might not start.

 

Could you take a video of what's going on in the car during startup?

It is necessary to understand at what stage you have a problem.
Starting a hybrid car is quite a complicated thing, it does not happen like in a regular car (insert the key, turn the key and the starter starts to spin the engine).

 

From the video, the car sees the power button push, else the voltage wouldn't drop like that. The dash lit up once when the OP first took possession (first post). Was that both the combination meter (dashboard) and the MFD? Failure of the combination meter to light up is a very common problem on these cars, but it is separate from the MFD not working. There is a very long thread on it here:

combination meter repair - DIY | PriusChat

Combination meter failure doesn't normally keep the car from starting, but it often makes turning it off difficult. (Rather than a single push to turn off, one must hold down the start button for several seconds. Like a forced power off on a PC.)

The OP reported having checked the AM2 fuse, but not the status of the others. It would make sense to check all of the fuses. That said, I'm wondering if rather than a bad fuse this isn't a bad relay. I don't have the electrical diagram for this car handy but in most vehicles there are one or more relays which need to click in to connect power from the battery to the various other electrical systems. If those relays fail, the car will have problems, usually big ones, very much like what is seen here.

Is it possible to read codes, preferably with Techstream or an equivalent?

After the car is started, is there 12V at the power outlet under the glove box? If not, perhaps start by working that problem. It should be a relatively simple circuit, and if that starts working perhaps some of the other problems will be resolved too.

 

There is no hybrid part connection and the "ready" sign - the socket will have 12V battery voltage.
There is a connection and the "ready" sign, then the socket will have about 14V.