Original motherboard component + redesigned PCB = Well working?
Redesigning a PC motherboard would take vastly more time and money than just buying a new laptop. The board has many layers and hundreds (if not thousands) of traces. You will not be able to figure out all of the connections. Even if you could, you would probably not be able to buy all of the same components unless you desolder them from the old board. That requires a hot air workstation and experience with surface-mount technology. The workstation will cost hundreds or thousands of dollars.

If you somehow design a new board by yourself (which would take a long time), you will need to build it. Prototype boards of that size and complexity can cost thousands of dollars. Once you get the board, you will probably find that it doesn't work very well. Gigahertz-class signals require special layout techniques.

Like Matt said: if you have to ask the question, you can't do it. It's like trying to build your own skyscraper because you want a bigger house.