Ok, so I tore down my screen and got to where Enejus got. If you feel up to it, here is how to actually get to the circuit board and resolder the connection.
1. Open up your iMac and take out the LCD assembly. (I am sure you can find a guide for this step.
2. Locate the faulty connector, on the rear of the screen, bottom left side. The white connector will probably pull out like mine did.
3. Swear because there is no way you can solder it back in place and the jamming it in place idea is probably not a good long term solution. Here is how you get the clearance required.
You need to get to the other side of the connector like Enejus did.
1. Start by tearing away at the metal tape all around. Do this carefully as there are sometimes multiple layers of it and you might tear a connector.
2. You want to remove the outer mounting brackets. They are held in place with 8 torx screws and glue. Once the screws are out, you'll have to carefully pry the brackets off, make sure you aren'y using any sensitive part of the screen as a leverage point.
(note the screw hidden behind that metalized foam)
3. Take off the metal cover over the lcd logic board (top). (4 phillips screws)
Be careful as a bunch of really really small wires will now be exposed.
4. The outer metal trim will now be freed. However, you'll have a heck of a time prying it off. Raise the screen by supporting it on the LCD. Use some large books to distribute the load...we don't want to crack anything.
5. Pry off the metal trim by inserting flat head screw drivers at the dimple points. I found it easier to start at the top of the screen.
6. Ok, now watch out. There is nothing holding the LCD panel in place now...if you move the screen, half of it will come with you, and the LCD panel will stay there. We now need to take apart the light guide, it's held in place by that black trim. I believe there are a few screws holding it in on one side, and tape on the other. Start by removing these screws and the tape.
7. We can't simply pry off the black trim, as it holds a whole bunch of defusers, the light guide and reflectors, and, sadly, the connectors from the LCD driver to the LCD screen go over it.
I tried to remove the circuit boards, but they appear to be glued in place. Luckily, we can "unroll the connectors". See next post.