If everything is securely plugged in and nothing is being pinched then it doesn't look good, downer
Yes, downer. It was both the lamp and the cable, changed the lamp and made workaround with a single wire. For a while all worked nicely, but then new lamp failed again. I thought maybe it's because I wasn't too careful when replacing, could be that a part or one end of the lamp was pressing against plastic or maybe metal case causing too much heat(?). Then I got another lamp and broke it while replacing. That was it. I had to give up on this, as it was already too much time & money spent.
Lesson learned. Do not replace lamps on a notebook screens, get a new screen instead if possible.