Ooooh this is bad. PS3 controllers are not meant to be opened.
I'll explain why. The interface with the buttons to the controllers mainboard is literally soldered on before its insolated.
If you don't know what this is. Here
now when you take your controller apart, everything seems so great and easy, it almost literally falls off, right, Wrong, what actually happens when that strip comes off is this. The conductor that's on that circled area gets torn off and stays on the board. Take a look at your strip, if it doesn't look like solid stripes with absolutely no differences between the stripes. you're lucky.
When you put the controller back together, I'm going to assume you have decent experience in connecting wires and things, when you put it back together, you may not have put that precious ribbon in its right place(because it tore off there's almost no way for it to stick to the board anymore) so that may be on the wrong nodes. causing your buttons to not work(hence why it wont power on(if you put it together right, try squeezing it really tight before pressing the PS button on your controller and it may power on)
the only way you can fix this
A: your precious ribbon isn't damaged so bad that it can still pass a decent connection to your main board. In that case, simple hair dryer on the plastic can make it slightly adhesive, but its best to find an efficient way to lock it down in place. your controller will work once more. but don't open it again.
B: your precious ribbons conductive cable was ripped off the ribbon when the controller was taken apart, which is bad, BUT, if you carefully use a small screwdriver, you can grind away the insulation on the ribbon and the main board and try to press it down again. Be freaking careful. this may just get your controller a second life.
C: replace the plastic ribbon. you can replace it. its not expensive either, just be super careful in putting it back together, as far as i know, but don't quote me on it, the ribbon you buy comes with, or is already sticky with a non conductive adhesive. still its easy to replace the plastic if you feel that you may damage your controller in an effort to fix it.
Carefully take it apart and see which side of the connector is damaged.(if any damages) Send photos to this thread, and i will tell you which side to scrape away the insulation.
Best of luck