Step 1: Oh No
Your controller seems broken if it doesn't turn on... First check the batteries to see if it works using a battery tester. If you don't have one then you can just replace your batteries. In my case the batteries are fine... If they still don't work.. Then read on!
Step 2: Get a Tin Foils
See here that it won't light up get a fat piece of tin foil and a fat piece of toilet paper or napkin.
Step 3: Put the Tin Foil
Put the tin foil as shown
Step 4: Put the Batteries
Now put the batteries in flipped since the case goes upside down
Step 5: Put in the Toilet Paper
Now put the toilet paper so the batteries won't come out
Step 6: Your Done!
Now just put tape over the batteries (you don't have to but be careful with it) and just press it and BOOM it works if it doesn't move the batteries around