I agree with MM about repair problems.
However, needs must when space is very tight, so I got a Lenovo ThinkCentre M71z (SNTA6UK) for one of my children, whose room is "bijou", and desk / floor space is at a premium. A laptop was tried and found wanting for the particular situation.
It has a good, basic spec. (I don't particularly want to encourage games on PCs that are primarily for schoolwork), includes built-in wifi, comes with Win 7 Pro x64, and the hard disk, memory and CPU are all upgradable, and easily accessible.
If the screen goes there's a VGA out!
£455 including delivery & VAT.
SD