Can broken edp cause no backlight?

The answer is yes, the eDP cable carries power and ground to and from the backlight. 

Hopefully the "fix" was limited to a damaged cable and not a damaged power circuit to the backlight, but you will need to replace the wiring harness to tell for certain.

Power circuit backlight can be repaired if the problem not fix with replacing edp cable?

And another things that i forgot to say sometimes monitor doesnt turn on at all

If the problem turns out to be the high voltage circuit on the system board, no -- it's not repairable, at least not economically.  Finding the faulty parts is difficult, and finding replacements, unless you live in Southeast China is just about impossible -- factor in the labor, skill and equipment and it'll be less expensive to simply replace the system board.

You know the side of broken edp is where connect to laptop monitor. It means that the side of edp cable that connect to monitor has problem no where connect to motherboard. can it cause laptop monitor cause backlight and need to replace monitor?

Same question, same answer - the eDP cable carries both power and ground to and from the backlight.  If the cable is broken, replace it. 

If that solves the problem, you're set. 

If not, you may have a damaged display or system board.  You'll have to tackle those one at a time thereafter.