Can I take it the computer actually works ok? How long after it being on does it take before this beep occurs?
A long shot, but it could be an alarm that gets triggered when the core temperature gets too high. If this is the case, you can pick up extra fans for a few pound from Maplin. The bearings often fail after a while (maybe several years..).
Very often though, a good clean is all that is required, a can of compressed air, clean those fans and grills, airflow is crucial.
Paul