Is it safe to put a new fish into a tank where other fish have died recently?

[Amanda4990]

A couple of weeks ago I got a new fish tank, gravel, heater, filter, etc. with 6 fish. I did everything that I thought I was supposed to do. I put dechlorinating drops in the water, kept it at the right temperature, etc. Within the first few days, two of the fish died, and over the past few weeks, one by one they have all died. I would like to start over and perhaps just get a goldfish instead of dealing with multiple smaller fish, but I don't know if it is safe to put a new fish into this tank. As far as I know, my old fish did not have ich (I did not see any signs of it) but perhaps they had something else? I just wanted to know if it would be safe to put a new fish in this tank without changing out the water. I would like to keep this water since it has already had a chance to cycle out and establish bacteria, etc. What should I do?