Ebay has motherboards starting at around $100, but pretty much every place that carries them is going to be AS IS or buyer beware. And there will be compatible models without the GPU or perhaps a faster CPU, so you could upgrade that way as well.
Installation is another matter, if you are willing to do it yourself it would just be your time plus the cost of the motherboard. A service center is going to charge you a few hours of labor, so several hundred total at least (but then you don't have to worry about buying a motherboard.
You have to weigh that against the convenience of just buying a new or used laptop.
A quick look at the motherboard doesn't look like it has any connections that you could add an external GPU to. Basically need a PCIe slot (M.2, or like a wifi add-on port.) External GPU mods are cumbersome anyway. Exposed wires, drilling holes in the chassis.
More expensive computers with thunderbolt or even USB-C with PCIe, etc, make external GPUs a possibility. Still not entirely desirable.