I work on laptops almost every day.
Most laptop keyboard cables are not solderable (they are like M membranes).
In truth, it depends on the laptop. Some use nice gold plated ribbon at the end of the connector that you can solder to. Most are just the end of the bare membrane.
Your best bet is to buy the "other" end of the connector (the one on the motherboard) and solder to that.
Based on your description, it sounds a little like a modern Dell (or HP) controller, where the KB matrix plugs into a controller, which then plugs into the motherboard. I believe these output USB natively to the MB, and might carry extra power for the backlight (if present).
Basically, I will need more info or a picture to best advise you.