A motherboard allows all the parts of your computer to receive power and communicate with one another. So a bad mobo can certainly affect other parts of the computer. The processor (CPU) is just one part of a modern mobo. Other parts include RAM slots, chipset, BIOS, connections for video and audio, USB ports, hard drive interface, etc. A power surge, for example, can destroy the electical connectivity requiring that the entire mobo be replaced. What is a Motherboard?
Depending on how much it would cost to replace the mobo (actual cost of replacement unit, then the technician's time and labor to install and test) it could be cheaper to buy a new machine. Especially if it turns out that other parts were damaged as well.