Hi Pauline.
There are a couple of potential problems.
You say you have just set the the tank up - did you cycle it with ammonia before you got the cardinals? If you didn't (and quite probably don't know what I'm talking about

) you are now doing what we call a fish-in cycle.
Fish secrete ammonia - they breathe it out and excrete it. The problem is that it's toxic to fish. It burns their skin and gills making it hard for them to breathe. In a mature tank there are bacteria in the filter which turn this ammonia into nitrite - but this is also toxic. It binds to the fish's blood making it hard for them to absorb oxygen. In a mature tank, another species lives in the filter which turns nitrite into nitrate, which is only toxic at high levels. These bacteria take several weeks to grow in a process called cycling.
Because the amount of ammonia will build up and up while these bacteria start their slow growth, you will need to do lots of water changes to get rid of it until the filter can cope. Then once there are some ammonia eaters, they'll start making nitrite and again you will have to do water changes to keep that low as well.
The first thing you need do is daily water changes of at least half the water, making sure the new water has dechlorinator added and is warmed to the same temperature as the tank water. As soon as you can get one, you'll also need a test kit. Liquid ones work out cheaper per test, and the stes contain an ammonia testre which the strips don't.
Once you've got your test kit, you need to test the water at least once a day and do water changes every time you see ammonia and/or nitrite getting near 0.25. That's the maximum safe level for both. Eventually you won't need to do these water changes once the bacteria have grown.
Here is a 'how to' thread going into more detail.
http://www.thinkfish.co.uk/forum/index.php/topic,17.0.htmlThe other problems you have is that the tank is a bit too small for cardinals. They need a tank at least 60cm long. To be honest, a shoal of something like ember tetras or a group of male endlers would fit in your tank better. And they are new - fish often act oddly till they settle in. Shoaling fish often have an alpha fish. When they are removed from their shoal in the shop tank they have to sort out a new alpha fish for their new, smaller shoal. This could be what you are seeing. Once they have sorted out the pecking order, they should settle.
You also mention having an ornament - do you have any plants, real or synthetic? A lot of shoaling fish need hiding places. It sounds backwards but they come out more if there is somewhere for them to run and hide if they feel threatened. Without this reassurance they tend to cower in a corner.