The aircraft was approaching Adelaide from Melbourne having received an airways clearance for descent to 3000ft, with a pilot's intercept of the runway 23 localizer. Approximately 46km east of Adelaide the DME reading disappeared from the FMS CDU. The captain then selected the appropriate "FMS fix" page to reinsert the data which caused a "time out resynch" message to appear on the FMS CDU. It was the crews first flight into Adelaide and a correct approach briefing had been given. Weather conditions were perfect, the wind calm with no cloud and unlimited visibility. The captain stated that due to the FMS problem, both he and the first officer, who was apparently hand flying the aircraft, had had a momentary lapse in monitoring the approach, and allowed the aircraft to pass through the localizer. The first officer noticed the runways of an aerodrome immediately in front of them, notified Adelaide Approach that the aerodrome was in sight, and reacted instinctively by commencing a right turn for base leg to what he believed was runway 23, without descending below the cleared altitude of 3000ft. The error was immediately recognised by the crew, at the same time Adelaide Approach advised "wrong aerodrome". The aircraft had been positioning for Parafield, a general aviation airport situated 20km north-east of Adelaide, and was then turned back onto the localizer for a landing on runway 23 at Adelaide. The captain said that if weather conditions had been different he would not have spent time rectifying the DME fault, but would have completed the flight monitoring the navigation instruments to Adelaide via the 23 ILS. He is to submit an ASIR to his company on return to the United Kingdom, with a recommendation that Parafield and Edinburgh airports be highlighted on company operational documentation.