Battery, powering steering and dash lights not working properly

I went out to take my daughter to school, started my car and I noticed all my dash lights were on and it was flickering like the radio, dash keep going out, then back on every 2 seconds and had no power steering. I turned the car off and tried to start it just clicked like battery was drained. Went in to get my tester and battery is fully charge. I tried to start it and it started right up but the same issue occurred. I checked fuses and all were good. Tried to start again and it just clicked like the battery was drained. But the battery is still charged. I'm thinking if the battery isn't draining then it can't be alternator but I'm not positive. Please any help would be greatly appreciated thanks.