Hey :)

I would like to see some drama/movie, where the male lead (or a significant supporting character) has some kind of inner conflict (the more the better xD.

He should be at odds with himself and have some emotional scars, maybe from abandonment or some other trauma.

My request sounds kind of creepy, but I like darker dramas /movies. I guess most of the highest rated shows on my list, fit my request.

If possible, the romance should be not a major theme.

Nice guy and Triangle have male leads with tragic pasts and lots of depth to their characters. Def not fluffy kdrama stories
Already seen, but thanks :)
Baker King Kim Tak Gu? :)
I see that MARS is on your to watch list, that's probably the epitome of this kind of genre, for both leads. It's definitely worth a watch (definitely the Taiwanese version, the current Japanese one is very condensed). 
Hi 

I think you might like

Pride and Prejudice (4/5)
Gap Dong (4/5)
Hotel King (4/5)
Bad Guy  (4.5/5)
Sorry, I love you (4.5/5)
Punch (5/5)

Enjoy, Luna
Sirius
Himizu
Clone Baby
Moon Child
Piece
N no Tame Ni
Bleak Night
Kurosagi

I +1 MARS. First, because it's a must-watch all-time classic of drama awesomeness. Second, because the male lead AND female lead fit your profile and trust me, it's DARK. 

On another level, have you seen Othros no Inu ? It's ALL about male leads having inner comflict (A good guy having the power to kill with one touch and a bad guy having a power to heal with one touch, both trying to influence each other.)
Thanks for all your recommendation :D
I've seen many of them already, but there are a few I will give a try :) I'm currently watching Mars and I'm hooked even though I should do my papers for university xD
@Juniko I've seen Othros no Inu :) It was one of my first dramas and I absolutely loved it ^^
of course, for your criteria... Soredemo Ikite Yuku :D

the others

Missing Noir
Arifureta Kiseki
Date
BORDER
master's sun
I remember you
byakuyakou
N no tame ni
kill me heal me
its okay thats love
bara no nai hanaya
yasashii jikan


Based on what you haven't seen that i highly recommend:

Thank You (such a tear-jerker)
Ghost (crime,mystery,technology and most importantly So Ji Sub!)
The Devil (EVERYONE has some kind of inner conflict)

Hope this helps!!