Using a Button to Sequentially Turn LEDs On...Confused

I don't think you have understood how a switch/case works. You don't need all the ifs in there.

Have a look at the tutorials for switch/case https://www.arduino.cc/en/Tutorial/SwitchCase and https://www.arduino.cc/en/Tutorial/SwitchCase2 and see if the examples look anything like your code.

Steve