Is my Goldfish depressed?

[Mazzi]

Ok so I've had two gold fish for about six years now and the other one got sick and eventually died.. Died at the bottom of the tank on its back. The other fish kept nudging it to get it to move. I took the dead one out and the live fish wouldn't move out of the spot the other dudes in. Bought another fish and it seemed ok at first.. Until a couple days later I found the new one dead. Since then the old one hasn't been the same. He won't leave the spot the ofiginal one died in, he won't eat, and he's changing colors! Reach in the tank to touch him and he doesn't move from that spot. I feel like he's going to kill himself.. What do I do? Should I put him out of his misery? They say fish have no feelings but clearly they do

 

[OrangeCones]

Goldfish (or any fish) do not 'kill' themselves due to 'depression.' Something is wrong with the quality of the water he's in.

What sized tank is it? What is your water change schedule like? What are the tank's readings for ammonia, nitrite and nitrate?