Well the basic idea is that you need to add a new button to the end of that ribbon that will take the place of your power button if you can no longer connect your original power button again.
However it is much easier said than done, especially with the small circuitry that is in laptops. If you havent done anything with hardware circuits before then a laptop is not the place to start. If you have worked with circuits before then you need to find out which cable in the ribbon is the common ground and which is the pin for the power switch, the. Add a switch or button between them. I don't think I have ever seen a laptop manufacturer publish the specs for internal wires so it will probably be lots of guessing and checking.
Overall, unless you are planning on spending a significant amount of time on this project you are going to end up with something that looks and works mediocre at best. It's just not an easy project working with tiny laptop components.