My dad has a 1998 Lexus that isn't used very often and so the battery has gone flat a number of times. He now leaves the battery on charge periodically. However, today he found that the car battery would seem to be completely flat - no response to key fob even - but the charger is showing the battery as fully charged.

The charger is a Halfords Fully Automatic one and testing it on a neighbour's car seemed to show it was working OK (His car hasn't been used for a while either and the charger showed amber).