why when I touch the input cable or put my hand near it the LED comes on?
It's because your button pin is floating (susceptible to ambient electromagnetic interference). When you wave your hand or touch the power, the button pin might sense random voltage that could be in the "high" range. 

Think about how the button is connected internally:



So in your schematic, all that second resistor is doing is draining a little current from power to ground, when it actually should be functioning as the pull-down resistor for the button pin.

Solution:
If you move the right leg of that resistor over two holes to the other side of the button, it should work.