Fish are dying need help!!?

We bought a 3 gallon aquarium and bought 2 fan tail gold fish to put in there along with some ph balancer and bowl conditioner and test strips. we tested our tap water and it was extremely hard. (NOTE: we had fish tank set up at least 2 week before we bought the 2 fish.) after having the fish in there for at least a month the water started looking really murky so we changed the water and placed the fish back in the aquarium and after 2 days both were dead! (NOTE: this has happened 2 times in the last 2 months) Would it be safe to use distilled water? or what do we need to do?