The motherboard that works with it is the one it has. Very little modularity between laptop chassis. Usually purpose built, any motherboard swaps supported would effectively be buying a whole new computer, might as well just find that model for sale on ebay.
You might be able to upgrade the CPU if you don't mind taking it apart, depending on the CPU it has now. Otherwise, the basic normal upgrades of memory and drives are your options. An SSD is never a bad idea, that can make quite the improvement to the desktop experience.
Buying parts for it, while seemingly cheap, is going to add up with shipping and all that.
Depending on the use case of your family member a cheap tablet or chromebook might be a good alternative. If it is just basic PC capability, you can also look at Intel Atom based netbooks. They also sell Atom processors in stick format(google stick computer), all you need at that point is a monitor or TV and peripherals.