u'll hav to definitely solder it on, but first u have to remove the main board(pcb) to have enough room to do the job. remove the old on/off flex by unscrewing the 2 screws on the top right power button,reheat the flex for few seconds to remove it easily by heat gun and then remove the 3 screws on the volume button there u can take it off. replace the new on/off flex the same way. assemble the rest of the board and solder the flex. hope this will help.

PROBABLY THE PROBLEM IS WITH THE LCD QUALITY YOU HAVE BOUGHT BUT CHECK FIRST THAT THE SURFACE OF THE LCD FRAME IS CLEAN WELL AND YOU ARE USING THE RIGHT STICKER (not so thick) during assembly coz, it will cause blotch when lcd surface is press. hope this will help.

just remove and reinstall main battery connector to reset the system then it will come the backlight on your lcd