You're talking of the power switch cable (blue & white wires) and connector . Is the socket desoldered from the logic board and still attached to the cable ? If so, try to find the socket location on logic board (upper left on the board). You will see two small contacts points so place the socket on these two contacts and check where the white and blue wires goes on the contact points. Write it down on a paper. You can't solder back the socket on the logic board but you can solder the blue and white wires directly on the contact points that why it's important to know their locations for polarity stuff. Now cut the two wires, strip them a bit and apply just a little solder on the wires ends with the solder iron then put each one on their specific contact point on the logic board. Apply briefly the solder iron tip on the wires ends to solder them to the logic board and that's it. Use a tiny tip cause it's really micro soldering stuff. Make sure to not bridge the two contact points. If you want to do a better job, find two wires of the same size and solder them to the logic board then fix them inside the iBook bottom case to secure the logic board welding. Then buy mini connectors (male/female) to connect the blue and white wires to the already soldered wires so your top case can be completely separated from the bottom case.
You may also apply hot glue to the two solders on the logic board. That will secure the solder job.
I hope the explanation is clear for you. Excuse my poor english writing I'm a Quebec francophone doing my best LOL...