the camera cable socket if definitely fixable I have done this many times. It is not for the faint of heart and you will definitely need a scope and fine tipped soldering iron to do so. I would not attempt to take the glass off the front of a unibody Macbook Pro unless I was prepared to buy a replacement. I broke the first three that I tried to remove myself...Replacement glass runs around $50. I have never heard of a faulty camera causing high fan speeds. I have seen some funny problems when a USB circuit is shorted, although it usually just causes the computer not to post. Can you post a high res picture of the connector that is broken?
I would put a spare HDD in the unit and attempt to install OSX on the second HDD. You can more than likely use Migration assistant to get your data back after the install. If you do not have a spare HDD you can pull yours and hook it up to a PC and run the manufacturers hardware test utility on it.
that clip attaches to a nub that sticks out from the inside of the bottom case. It does not need to be replaced, however the bottom case will have more flex to it if you do not replace it. look up ebay item number 250711661655 for a replacement. The only ones I see available are in the UK.
through a scope push on each connection and make sure they are all actually connected. There could still be flux inside the connector. You can get aresol flux cleaner from some electronics places that does a great job of flushing flux out of sockets and what not as it comes out of the can with a lot of pressure. You should also look at the traces and see if any of them go to a drop in the board exceedingly close to the connections that you made. Now that the connectors are on the logic board you might also want to heat up the whole connector to the point that the joints reflow. You can not do this with a regular heat gun, you would need a BGA machine to do this and not ruin the connector or any other plastic components on the board. You should double check the work, however judging by how they all both the same problem an issue with your work is probably not to blame. You should also ask the owner of the units if they had the problem before you brought them in.
If it is not posting chances are the HDD is not the issue. I see if it posts with an external monitor first. If it was in an area that was subject to extreme temperature swings something may have happened to the LCD. This logic board does also have an ATI graphics chip on it which I have problems with in the past. Generally with apples the beeps coincide with flashes from the power LED so if there are no flashes I would say it is not throwing a beep code. If it does not post externally I would take it apart to to expose the BGA chips and try to heat the ATI chip on the board up and see if it posts then. Use a hair dryer or heat gun but do not go over around 175C. You are not trying to reflow the chip just heat the connections under the chip. I have used this method to see if there is a BGA issue quite a few times. You should be able to just short the two points in the connector that the power plugs into to start the laptop up so you do not have to put it all the way back together again. You could also...
I have one here that says LDPR on the top line and underneath it says 060I. I recommend using a heat pump to replace this chip. I hope you have flux as well. You might need to bring the temperature up to 350C to get the component off.
I have seen this issue in laptops before and it almost always ends up being a short in the headphone jack itself. I have not personally taken apart one of these so I can not say if the headphone jack is on the board or connected to it. From the teardown it looks to be on the logic board. you can also pull the battery and try to flush the jack with alcohol.