Did you cycle your tank before putting in the new fish? Many times new goldfish owners just fill 'er up, turn on the filter, and pop in a bunch of fish at once. What they don't realize is at this time (usually for the first 1-3 weeks) an invisible war is going on. Good bacteria is fighting the bad bacteria to establish the colony, and at this time water parameters are in complete chaos. Cloudy water is typically a sign of this happening, usually referred to as a bacteria bloom. These ever changing water circumstances are very dangerous to goldfish, especially during an ammonia or nitrite spike. Before adding in new fish for a while, get your water tested once a week for the first few weeks at your local pet store (most provide free water testing for their customers) or do it yourself by buying a tester kit. Running the tank for a while to let bacteria colonies establish is referred to as the "fish-less cycle". Otherwise, you can end up with a bunch of problems, such as "new tank syndrome" which includes a symptoms of loss of appetite, black smudges (ammonia burns) on body, and usually sudden death.

Another cause of fish deaths early on could be that you are overcrowding. What size is your tank? For 4 goldfish you should have a 30-40 gallon tank (rule of thumb is for every 10 gallons you should have 1 fish, though sometimes with a lot of filtration and water changes you can squeeze them in). Overcrowding mixed with poor filtration mixed with unpredictable water parameters is a recipe for disaster.

Also, what kind of water conditioner are you using when you make water changes? You should be using something that removes chlorine and chlorimines (like Aquasafe) if you are on well water, and if you are on city water you should use something (like Amquel+) that takes out ammonia, nitrites, and if you are on city water. What many first-time pet owners don't realize is putting a fish in water that is treated without proper treatment is also deadly to fish.

Hope this helps

Goldiegirl pretty much covered it all
But I would like to emphasize the importance of proper stocking of your tank. You can't think that the fish are "still so small!" because goldfish tend to grow very fast, and very big. They also produce a lot of ammonia, so you need to make sure that there's enough water for each fish to swim in, and so that the ammonia and waste products won't be too concentrated in the tank.

Also, remember to buy a water conditioner and a test kit! It's important that you test for ammonia every day for the first two weeks, later for nitrite and finally nitrate. Do water changes whenever the levels get too high, about half would be good. Make sure you have a good biological filter to deal with the fish waste as well! It should turn at least 5 times the tank volume per hour.

Now, good luck with the fish!

Here is what I posed a few weeks ago to sbdy else, it explains the cycle

 Re: Help new gold fish will not eat
« Reply #4 on: August 27, 2010, 02:31:00 PM »   

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Please don't get discouraged, we'll help.

First you should remove the left over food as it pollutes the water.
... and with this we can start and talk about the Nitrogen Cycle and cycling the tank   ... may sound scary but it is easy...

OK, lets get started:
1. Fish produce waste with their poop, etc. Plants decompose ( dead leaves ) uneaten food decomposes. All those produce Ammonia which is highly toxic to our fish.  It is like swimming in sewerage.
2. to break Ammonia down we need beneficial bacteria. They brake it down into Nitrite which is still toxic to fish.
3. to break Nitrite down we need beneficial bacteria again which brake it down to Nitrate ( which is only toxic to fish in high concentration )

To control the cycle there are test kits available. I use the API Master TestKit for freshwater it contains all tests for Ammonia, Nitrite, Nitrate and pH. If you start cycling a tank ( planted with some live plants and add beneficial bacteria and some fish food but no fish ) Your tankwater will go a bit cloudy, which is normal. It means the beneficial bacteria try to find their home.

Ammonia will show first. After a few days it will start to go down and also Nitrites will spike. You will need to do some waterchanges, about 50 % but don't clean the filter as most bacteria establish in there and in the gravel. Keep adding beneficial bacteria, also a water conditioner every time you do those waterchanges.
After another while Ammonia will go down to 0 ppm and Nitrite will go down and Nitrates will show up.

A tank is cycled when Ammonia and Nitrites are both 0 ppm ( parts per million ) and Nitrate shoudn't be higher than 20 ppm, ideal between 5 -10 ppm. At this point it is safe to introduce the fish: one at the time for beginners 

Now, here is where the plants "function" kicks in as well. Plants love Nitrates to grow. They also use up Carbondioxide which fishes produce. They need it for their Photosynthesis and they return Oxygen into the water... for fishes to breath 

This is the basics how this small ecosystem works in the tank.

Hope it doesn't sound scary.
It is really not hard to test waterquality and do waterchanges.

According to Spaz not eating it is because he suffers in the bowl and gasps for air.
You also can try another type of food, as fish love different diets. Also feed only very, very little. If there is some food left after 5 min, remove it. For starters get some hornworth he may like to nibble on this plant. And a pump and an airstone to put in the bowl. Test the water and change 50 % of the water daily if necessary. Add some beneficial bacteria.

 

Isn't that a koi? I can see those little feeler things they have.

Ohhh lol yes that is one mighty big goldfish 

Wow that's a huge carp of some kind...maybe a koi, a fat one for sure!