Modern printed circuit boards often require special tools and solder. They are not designed to be repaired. You could try and find a mother board, but laptop mother boards are very specific. You would need an exact replacement. They are very expensive. Unless the laptop is under warranty, it probably is not worth repairing. You might be able to salvage some components like the RAM, Hard drive, CPU, maybe the screen and try to sell them, but even then I doubt you would get very much.
As much as I hate to throw things away, that maybe your best option. Please try to find a electronics recycling facility that will properly dispose of it instead of tossing it in a landfill.
Your understanding of layers and PCBs seems to be a bit off. All components are simply soldered to the surface of the board. There can be signal layers running through the mid planes, but these are connected to the surface with vias. It's a very easy task to replace SMT components on motherboards. The main issues though is why it originally burnt out. – cybergibbons – 2011-08-30T09:35:47.013
1Additionally, you'd have to trace down the "why" of the burned IC. If it's not something simple like the just that IC, the battery or power supply itself, you could be replacing it multiple times in the attempt to isolate what component failure is the root cause. ICs don't normally fail in this manner, typically it's another failed component elsewhere that cooked it. – Brian Knoblauch – 2009-12-22T20:45:22.937