I opened my ds lite to change my super scratched screen with a new one but in the process a little black square that holds a screen cable came right of and when i tried to put it in it broke in 2. Now the touch function of the touch screen doesn't work, is it because of the square and is there another way to fix it without that square. this is the square(this isn't my ds)
No. You will need to replace the logic board. The touch screen will never work properly if the cable clamp has been broken.
I am not aware of anywhere that you can buy a new logic board. Typically, people buy broken DSes with busted screens and other problems that aren't logic board related, but that is an "iffy" proposition because it's sometimes difficult to tell if the logic board will be fully functional. At this point you don't have many options, 1)Take your chances on finding a working logic board in a bad unit 2)Send it into Nintendo and pay them for repairs 3)Chalk it up to experience and buy a new DS