Are you familiar with the nitrogen cycle?
It sounds like you let the tank filter run for a week, but that is not a "cycle." when I first got my tank I went to petco and a guy there, speaking with utmost authority, told me that letting the water cycle through the filter was "cycling." it's not!
My guess is that your tank is at the nitrite portion of the cycle and your fish are having a hard time. Have you done any water changes?
Don't worry too much... All you have to do is search for info on cycling a tank, nitrogen cycle and fishless cycle.
Do a 30% water change. I say 30% because it is significant, but not too drastic... Make sure you have a water dechlorinator product before you change any water (Stress Coat is good as far as I know).
Then go straight to the shop to get an API test kit. I got the test strips and I'm finding they are not accurate. Although, they are better than nothing!
You've gotten yourself into a bit of a chemistry science project with fish keeping.
Here's the nitrogen cycle in a nutshell:
Fish eliminate ammonia through their gills. This is their waste, other than poop. There are bacteria present in your tap water that will eat the ammonia. Initially, there are not enough of these bacteria, but as they get more ammonia, they will increase in number. The bacteria will live on your gravel and in your filter. With a charcoal filter, you will want to NOT change your cartridge so that it will become a "bio filter." (google that term as well)
I got the thumbs up on my same filter setup from the guys at Wet Web Media, so you know this is good advice. I also have a sponge filter. Extra filtration is good.
Back to cycle: Once the bacteria convert the ammonia to nitrite, there are bacteria that convert nitrite to nitrate. Fish cannot tolerate ammonia or nitrite, but low levels of nitrate are normal. You remove tank water and put fresh, dechlorinated water in to remove nitrate. Live plants can help keep nitrate low.
It normally takes about 5 weeks for a cycle to complete from the presence of ammonia to conversion to nitrate. In order to speed this up, you can get some gravel or filter media from an established tank, if you know someone who will give it to you.
It sounds like your tank is almost through the cycle. Test your water for ammonia, nitrite, ph, chlorine, kh, and nitrate. If you are testing the water through the whole cycle, you will see a rise in ammonia, with no nitrite/nitrate. After a week or so, you will see the ammonia begin to drop and the nitrite begins to rise. Then the ammonia will go to zero, and nitrites will be high for 2-3 weeks. Then they will drop as you begin to see the presence of nitrate.
What makes this cycle take so long is that you will be doing water changes to keep your ammonia levels and nitrite levels down to a lower toxicity level for the fish. The test will tell you what levels are acceptable during the cycle and what is dangerous. If you do a fishless cycle, it will take much less time because you can turn up your heater and do no water changes. Search for info on a fishless cycle.
I hope this is helpful! If you already know all of this, I greatly apologize! It just sounds like, from your post, that you were unaware... Most likely from the fish store people misleading you. I swear it must be corporate policy to not tell customers about the nitrogen cycle so that you will not be afraid of having a tank. I bet it would scare off some people because of all of the actual work involved in fish keeping.
Good luck to you!