Ok looks like he on a 760g chipset, the onboard graphics on that really isn't much good for games
And it's a really cut down motherboard.
The options basically are
1 - replace motherboard and add it a graphics card
Issues with this, the windows license is probably linked to the motherboard, so swapping that out will also mean you'll have to buy a new copy of windows as well, the current psu is not good enough for the extra power consumption of a graphics card so that's going to have to be replaced too.
2 - find a pci-e x1 graphics card, will not be easy of cheap for what it is, best I could find was a 8400gs which is more a step sideways than a step up.
3 - build a new pc, going to be the most expensive option.
Going with option 1
Motherboard http://www.scan.co.uk/products/asus-...-micro-atx-vga
Graphics card (I've gone for under £100 here) http://www.scan.co.uk/products/1gb-x...-dvi-i-dp-hdmi
PSU (you'll need to check the size used I cannot find out if it's a normal ATX or some other size) standard ATX http://www.scan.co.uk/products/400w-...mm-fan-atx-12v
Windows 7 64bit http://www.scan.co.uk/products/micro...tem-single-oem (he should be able to use the OEM version?)
Total cost just short of £260
EDIT; he's got 3gb of memory already and his cpu while not the fastest should be ok and there's plenty of room there for later upgrades.
Current case, hard drive and dvd can be kept, a 2nd hard drive could be added for more space.