Those games don't cost a lot, pop along to GOG.com and get the DRM free versions of terraria and starbound, at least when they are on sale.
While some like starbound/terraria have Linux version but the Pi wouldn't do, Minecraft can be made to run, there is a long thread titled Minecraft.
The PC is where you need to be, it has the grunt to do it.
The laptops GMAs graphics will run it, just you'll need to cut back on things.
Minecraft runs well when you pull back some of the fancy stuff and you don't really notice after a bit.
Then buy a new motherboard, they can be had cheap to get you going, you don't need all singing and dancing boards.