I don't think the choice is that extreme.
From the specification (and the operating system) on your existing computer, the answer has to be that you could spend more on upgrading than a new computer complete with operating system and new everything would cost. If you did go the upgrade route you would still have a load of hardware that was 4 years old and subject to further failure
If you browse the Dell site you will see offers for complete computers from £300 upwards. They won't run the latest Doom 3 games but I don't guess that you need that. Just reasonably up to date, new with a warranty and operating system and able to cope with what the average guy needs a computer for.
Alternatively take a hike to PCWorld and look at the sale offers there. For what you say you want nothing over £500 complete is necessary