If your refill valve is always running -- even after being replaced -- it sounds like the water level in the tank is consistently dropping. The easy answer to this is that the flapper is not seating properly. Is the toilet new as well? Make sure that after you flush, the flapper falls back into place and seals against the seat of the flush valve (the white plastic part with the large tube extending from the bottom and middle of the tank). You might need to extend the chain of the flapper to give it more slack. A plumber's visit should have corrected what appears to be relatively simple, but you never know.