Nissan Pathfinder Battery Replace/Remove

I Left The Key On For A Few Hours And Drained The Battery. I Took It Down And Had It Charged. But There Is Still Nothing. No Lights ,buzzer...

I Have A 1998 Nissan Pathfinder With A Positive Battery Terminal Connector That Is Mostly Eaten Through By Corrosion. How Do I Replace This...

When Attempting To Replace The Battery, The Posts Were Reversed From The Original Battery, The Cables Were Connected And There Was A Short....