How much power does such a thing draw?
Could it be powered with a relatively small battery?
specialist low power x86 PC motherboards start at around 10Watts before you add things like hard disks, etc.
these cost a lot of money.
if you intend to use an old 2nd hand motherboard then expect to burn 50Watts minimum with a small HDD and minimal memory.
a 2nd hand laptop is a far better low power option but expect one of those to still draw around 20Watts. (although the battery problem is already solved.)