Unfortunately, it is highly unlikely to drive a Toyota hybrid with a totally dead hybrid battery. The hybrid battery is required to power the “starter” of the car.

If the battery is totally dead, the “starter” can’t work.

I use “starter” in quotes because it is technically an electric motor that acts as the starter, not a traditional starter like in a normal gas car or an older generation Honda hybrid. 

With that said, a diminished battery will still “start” the car. But it “starts” the engine kinda violently since it doesn’t have enough power. You’ll hear a loud thud sound when the electric motor engages and the engine takes over. It’s not smooth at all. And can potentially do more damage in the long run. 

(I ran my Prius a bit on a diminished battery before I could replace the hybrid battery.)

With that said, an older Civic hybrid from the 2000’s and possibly early 2010’s in theory should start fine without a hybrid battery. They have a backup traditional starter in addition to the electric motor “starter”.