There must be either a pull down or pull up resistor to make the switch have a known state when it is open. Otherwise it will "float" when open and the state is indeterminate. If you wire the switch to ground, then you can enable the internal pullup resistor. The switch input will read HIGH when the switch is open (not pressed) and LOW when closed (pressed). Adjust your code accordingly.
Change this line:
pinMode(BTN1, INPUT);
To:
pinMode(BTN1, INPUT_PULLUP);
and your code to look for LOW when the button pressed.
