I've reflowed a GPU on a laptop motherboard before to fix a problem (to reflow a chip though, the chip has to be attached to the mobo using a ball grid array (BGA), so you probably can't do it with the CPU, you could probably also reflow some memory chips), the capacitors could be replaced, some chips and sockets can be purchased online to replace the chips and sockets on a mobo.
However, when there is a problem with the mobo (maybe the laptop is not turning on properly or not turning on at all) and you don't know the exact part of the mobo that needs to be fixed, it's probably not worth it to try and fix the mobo, and it would probably just be better to buy a whole new mobo. The mobo can be quite expensive though, and sometimes it just better to buy a new, better, laptop altogether.