No winter start below 28 deg

I have no idea but maybe your big hybrid battery is getting weak if it's orig. I assume the 12v was replaced.
Cold temps reduce output from batteries. You could try various appoaches to keep car warmer (engine block heater etc).

 

If you will report your own post and ask it to be moved to the Gen 1 forum, you will find more informed readers than in a Prius c forum.
Generation 1 Prius Discussion | PriusChat

No one has any idea why they hide the Gen 1 forum, but they do.

 

I don't know where to start looking for the problem,
but maybe if you install a Engine Block Heater ( EBH ) and plug it in for maybe an hour or two before you start the car
it could help you get going until you are able to find out why the car is not starting when it's freezing outside.

This is where I got my EBH Engine Block Heater for 2004-2009 Toyota Prius - PriusChat Shop
And this thread says installation is the same on Gen 1 Prius 2002 Prius Engine Block Heater Installation | PriusChat

 

• Does the dome light illuminate when the door is open in the cold?
• Does turning on the headlights show beams?
• Do the headlights change intensity turning on the ignition?

Before going down the technical rabbit hole, perhaps you might share some of your background? You might also take a quick read of the sticky. We're going to help but we kinda need to know what resources you bring to the party . . . not to talk down but to address what we need to know and explain it so it makes sense.

Bob Wilson

 

When you say "nothing happens", does that mean the instrument panel remains dark? You need to be as clear as possible about which systems still work and which do not work.

As Bob asked, when you first enter the car, how bright is the overhead cabin lighting?
Can the headlights be turned on? How bright are they?
Then, when you turn the key from IG-OFF to ACC-ON, will the radio turn on?
When you turn the key from ACC-ON to IG-ON, do all dashboard warning lights appear? Can you raise and lower the power windows?
When you turn the key from IG-ON to START, what then happens?

Intermittent problems can be very difficult to figure out. In this case the car needs to be left out in freezing weather and someone (who doesn't mind being in the cold for an extended period) needs to figure out the issues and determine the root cause.

Depending upon the symptoms that are present, the issue could be a stuck relay. It could be a fuel pump that is frozen and refuses to run. Or it could be a bad ignition switch.