05 prius dash lights flash, won’t turn on

Did you buy a brand new battery? Whenever there's a no start issue, the first place to check is the 12v battery.

 

Not sure if my 2 cent comment will help.
Seems the problem is/ was intermittent.
Dash was working ever so often a few months ago, now completely failed.
Dash lights still currently work at start up then goes dark/ blank once the vehicle is started.

My comment...juggle the dash light brightness adjustment switch.
Sorry no greater lead than that, could be loosen connect behind the dash?
FWIW I do not think this is FOB or 12v battery issue nor a fuse issue, but inspecting the dash light fuse could be worthwhile.
Good luck hunting
Let us know what you find.

 

It sounds like your combination meter (CM) is in the latter stages of complete failure. This can be repaired at the dealer for about $800 or you can contact Matt @Texas Hybrid Batteries for their solution which will cost you ~$150 for a repaired unit that has a lifetime warranty, odometer programmed to your milage and when you return your broken CM back to them they will give you a refund of ~$75 for it. The only catch you (or a good friend) will need to remove the old and install the new one, which will involve the removal of some of the dash. There are YouTube videos to follow.

 

Which battery was replaced and how much did you pay?