My beloved Eee 1000H broke recently
But with the raspberry pi a resurrection might be possible!
There are many issues connecting up the raspi to the hardware, but it should be possible. Powering the device should be pretty straightforward, however, connecting the display might prove more of an issue since the screen is LVDS and needs some conversion somehow. Secondly, the keyboard and trackpad must also be connected. I have no idea what types of devices these are, but they might be able to be converted to USB devices, but this raises another issue: a battery powered USB hub to connect these are needed.
I have not got any expertise is this field, but hopefully others have similar ideas of bringing their old laptops back to life like this and will share their ideas. It could be fun to have the case ready for when the raspi arrives