Dash display out.

MFD screen in the middle, or the Speedometer dash area?

Unlikely it would be a fuse.

 

Without including the DIY fix option, this is the least expensive 'lifetime warranty' option : Prius Speedometer Replacement

If tearing into the dash isn't something you would enjoy doing, check on CL as there is usually someone with a listing for such.

 

Capacitors are known to fail, they can be replaced.

There are a few known 'tricks' that can ward off the failure, but at some point starting and shutting down the vehicle will be impossible.

 

Mine died about 5 times in 2 years, usually when the weather turned cold. It just happens, the reason that has been deduced is an under-specced capacitor falling out of tolerance. Replacing that capacitor offers consistently solid life for the combo meter after that.

 

Get used to sporadic operation. It will become more common, and eventually be inop for days or weeks on end before dissappearing forever.
There are a few diagnostic hacks that will "kick" it back into operation temporarily for awhile, but that won't last long.
You may eventually have to use the Push,Tap Tap method to shut your car off -- Press, and Hold your power button untill the MFD displays blanks, then double tap the button again.
.

 

White plug? Where near the battery. video on Youtube?

 

I had this problem and it would be random.

Once I cha he's the capacitor to a larger one, it 100% resolved my dashboard issue though, was a pain to take the entire dashboard out and only took 60 seconds to fix.

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