Sorry, meant to say I had to change both ball valves in both my tanks, as they decided to take it in turns to drip, had me scraching my head for ages, dont know if it helps??
Sound like your ballcock need replaceing, I had the same trouble with a build up of calcuim inside it so when the should have been off was still passing a dribble of water, adjusted it a few times with no luck. Quite easy and cheep to replace, just make sure you get the same size (and turn you cold ...
