It looks like the power traces lengthwise along the strip. If you gently pop the monitor out of the frame, you can probably identify where the contacts are supposed to meet up on the side of the monitor.
You may be able to use a very small dab of hot glue in the middle to keep it in place. Or one of the industrial boogers from a credit card offer. Power should follow the trace, so even if it has to go out a half millimeter, it should still conduct. Hold it down when you put it back into the frame, naturally.
It also looks like you only need that one trace from group to group. You could try bridging the pads on the monitor with a scrap piece of wire and see if that gives you power to the last 3rd of the monitor. If it work, solder the wire in and see if that give you your monitor back.