Charging System,Can a dead battery cause my engine to stop working?

I was driving and my car began to stall. Once I pulled over I could no longer press the brake down and the gas pedal would go all the way to floor but I could not move. I could turn the engine over once I tried starting the car again but after several tries to get my car up and running it would not turn over anymore. I could hear the normal clicking sound that indicates you have a dead battery.

I am confused because I was driving when all of this happened and I didn't think you could start a car if you had a dead battery.

My car has 67000 miles.
My car has an automatic transmission.