How to enable redstone wiring with a flick of a lever?

Solution 1:

I can see in your linked screenshot that you're using a slime block for some reason. Just a sticky piston on its own work work as well. And the slime block also tries to push the block below, which would push the block in front of that and in front of that and… It's basically trying to push an entire row of the world, which is much more than the limit of 12 blocks that pistons can push.

Just moving the piston forwards, replacing the slime block, would solve your problem.

Solution 2:

When the lever is turned on, the piston pushes the block out of the way of the wire, letting it sneak under the piston arm.
When the lever is turned off, the piston pulls the block back in the way of the redstone wire, and it stops working.

The concept is based on a simple AND gate, where the output is only on if both inputs are on. Like this:

For the redstone lamp to be on, the redstone trail must be on AND the piston must be extended. That's the whole point of an AND gate!

Learn more on the Minecraft Wiki: Mechanics/Redstone/Logic_circuit