The 7 connection goes to the wireless antenna sticker that resides on the back of the 3GS dock assembly. You can order the antenna on the net for cheap and iFixit has plenty of content on how to replace it.
Try taking a small thin copper wire with a small amount of solder on each end. Place it directly in the center of the logic board 7 female connection. Heat up the wire so the solder makes a solid connection on the logic board. Then apply generous amount of solder on the male 7 connection coming off the dock. Connect the two wires and you should get full reception on your antenna.
“I am so clever that sometimes I don't understand a single word of what I am saying.” Oscar Wilde.