By "proper performance" I mean that the LED cycles in intensity. But the LED is still always ON even when the arduino is not powered, and you're correct this was happening before.
Taking a step back, maybe I should ask if what I'm expecting is what I'm designing for.
I'm expecting that with power from the battery connected and the arduino not powered, the LED should be off. When the arduino is then powered on, the LED should cycle in intensity until the arduino is powered off.