Electrical issues 93 Corolla 1.6

We bought this car with the awesome intentions of my son and I fixing it up and spending time together. We have repaired several of the issues it had but have come accross one that has got me confused. We put a brand new fully charged battery in it and cant get it to turn over. Here is what happens. Stick the key in the ignition and tumble it over and all the proper dash lights turn on, stereo works, Brake lights did but now they dont. Head lights dont work and when you try to start the car everything goes dead, just like a black out. You have to turn the car ignition back to its original possition and retumble it over again to power back up. We dont even get that "tick "tick" sound from the starter. The battery load tested just fine so could it be a relay, or fuse, or maybe battery cable? We have cleaned the battery cables with baking soda and they look fine.

Help please.

Oh yeah, if the key is tumbled over and you press the hazards to test them, a buzzing sound comes from under the dash at the fuse box, but all the fuses look fine.

Thanks, Doug G