I know PC World comes in for some stick on these pages but to be fair when I had a serious problem with my computer the Technician who came to fix it at home under the 3 year warrenty was most efficient.
He found the fault with the graphics card straight away - the fan had fallen off! - and replaced it with a new one.
Unfortunately the computer still wouldn't work and he ended up replacing the mother board as well.
He did the whole job in under an hour which was quite impressive for an almost complete strip down and rebuild. He left me to re-install Windows and phoned me an hour or so later to see if all was well.