Which is supposed to set off a series of LEDs in a sequence
You might have some idea what this means, but I sure don't. An LED (pin) is either off or on. There is nothing sequential about that.
when the button is pressed and then off when pressed again
That looks like two states - pressed once and pressed twice. Your code has 4 states. Please explain the discrepancy.
What do your Serial.print() statements tell you is happening?
Why not?