2007 Toyota Yaris Power Steering / Dead Battery

[LoveAndLiveHappy]

This morning, after leaving a light on overnight, my battery was dead. I jumped it then upon pulling out of my garage noticed the power steering was weird. I drove a bit, then again - the power steering got real tight and the PS indicator light came on. I immediately drove to my oil change place, thinking maybe I need PS fluid, they quickly revealed that my car doesn't have a PS reservoir. I drove to the nearest gas/service station, because my fuel indicator was blinking that my gas tank was empty. As I pulled in the PS went out completely. I filled up my gas tank, then car wouldn't start again. The mechanic jump started the car and noticed the fuel indicator was still blinking that the gas tank was empty - weird. Anyone know anything about if the battery and power steering are connected in some way or is it just a coincidence? The mechanic kept the car and is replacing the battery (it's from 2012). He says he can't do much without being able to run the car.