I'm happy to tell you that I wíll be able to solve it, relatively easy even. The photo is with a quickly restored - but not yet permanent - connection.
like I hoped, a fresh pair of eyes - being my boyfriends' - led me to where the problem lies with the lighting of my laptop. At first he didn't know what he could offer with what I had already tried and had covered all possible problem-bases. But he came up with testing the lights seperately in a way I didn't think of (and with the knowledge of how and when to use resistors that were needed not to blow them up). That way it was fairly simple to figure out where the problem would most likely be.
which was in a connection that looked fine, but somehow isn't and shouldn't be too difficult to fix. Seeing the lights working again makes me só happy! And I'm very glad he could help me solve this problem.
I'm very curious if the light will spread more evenly behind the screen once I assemble the screenparts and close the sides. Then no light will go sideways like it does with this setup, but concentrate within a small space and hopefully you won't see the obvious lightpoints like you do now. The leds I used are bright enough for it (unbelievably so, with how tiny they are!), I can't wait to move on!