Logic Board for 3GS?

These connections are considered pressure connections. I have had this happen on iPads before with new techs, and when that happens sometimes you can rig up something and sometimes you can't. What I did when new techs had this issue was place the tab back into place if i could, take some electrical tape and tape it in place (if you don't have this, then a tiny piece of paper (2 or 3 layers over the metal pins will work). I then would add a few more lays of tape so that when we screwed the LCD back in it would add pressure allowing the connection within the digitizer clip, sometimes i did not need to do this and it would just work without rigging something up. In your case add some lays of tape and then close the phone up and put in the bottom screws, you can keep the phone on while doing this, so you don't have to keep turning it off and back on while opening and closing it, just be very careful, then see if the proximity sensor and ear speaker work, these can be tested with a phone call, the proximity sensor allows the screen to go black when your on a phone call, so to mimic this just cover the sensors with your thumb (left of the ear speaker), this can also be tested in the voice memos app that is a stock app from Apple. Keep adding layers of tape if it does not work the first time, and make sure that it is not too much pressure so it is ruining the LCD and pushing on the back of it (you will be able to see this when the phone is in use, distorted picture where the tape is), and you will not need a lot of pressure on it but you will need just enough, and when its all closed up the LCD will/should put enough pressure on the layers of tape to allow the phone to work properly. I wish you the best of luck with the repair!