Light switch no power when on
What you're trying to do isn't going to work

Judging by the extra Romex freshly brought into this box, it looks like you're trying to power an additional lamp or outlet from here, and specifically, from this here switch. 

Not gonna happen.  At least not the way you intend.   

However, a new thing changes the picture: Smart switches.  There's good chance we can save this.  

If you can pull the other switch out, and get us some photos of what's going on in the back of the box, we will be able to advise.  

Why you can't just pull wire to any old place

In the future, don't buy anything or pull the wire until you've figured out the circuit :) 

Your new branch needs "always-hot" and "neutral" if it's an outlet, or "switched-hot" and "neutral" if it's a lamp or fan.  You can't just assume those are going to exist in any given location.  

That switch is a 3-way switch, as HP discusses.  In 3-way circuits, the downside is they almost never have the 2 wires you need in any given switch location.  The upside is, they have extra wires, and with smart switches, we can take advantage of that.