The same happened to me on my out of warranty iMac 27 when I was replacing my defective super drive with a blu-ray player, where I lost a pin on the right side, and on the left side, eight pins were pulled off along with the left most pin pulling off a pad, and part of a trace. I have not soldered anything since I was a teenager, and I definitely have no experience soldering SMT, so I watched, and studied a lot of video on YouTube. This made me want to get back to my old hobby, but I have no equipment! I ended up buying a new connector from L2 Computer Inc on eBay, Aoyue 968A+ 4 in 1 Digital Hot Air Rework Station along with a bent nozzle from SRA Soldering, solder paste from Zephyrtronics, schematics from NotebookSchematic, microscope from MicroscopeNet, and a meter from a local electronics store. When I got my equipment, I did some practice soldering on a practice board, gaining some experience on how the hot air soldering work, and how the solder reacts, figuring out the correct temperature to use. I...
This connection is very fragile, and many people have broken the display connector on the logic board. You need to carefully pull the connector out, and when putting it back together, you need to carefully push the connector back in.