Confused on cycling (not cycling)

[DrHockey]

So I bought a 10 gallon fish tank 8 weeks ago. I didn't really know much about cycling the tank or fish in general. I ended up getting 3 zebra danios to cycle the tank. One is bigger than the other two so he chases them around. The other fish sometimes fight back where they go in circles and push up there fins. When the light is off they all school together and sleep I presume.

The problem is my aquarium won't cycle. I got the master API test kit and check ammonia and nitrite. The ammonia can get up to 1 and I do water changes to keep it down. I read how the cycle works and after 2-3 weeks nitrites are supposed to show up from the bacteria. There has been no sign of nitrites in my aquarium. I went to my local pet shop and they suggested that I might have missed the nitrite spike and I should test the nitrate to see if the cycle already started. When I got home, I tested the nitrate and it was at 0... It is almost like my filter, an Aqueon QuitFlow 10, won't grow the beneficial bacteria on the biological filter. Any suggestions from the community because these ammonia levels just keep going up and up.

[ScotJudd]

A couple of thoughts.
Firstly, fish in tank cycling is much slower than fish less because you are forced to keep the ammonia levels low to protect your fish. In fish less cycling ammonia is added to give about 4 ppm to encourage bacteria growth.
Secondly, the nitrite to nitrate bacteria a lot longer to establish than your ammonia to nitrite.
Lastly, are you water changing with conditioned water, chlorine and chemicals on tap water will kill the beneficial bacteria in your filter.
You could try adding a bacteria culture, there are many types on the market, but better still, do you have any fish keeping friends who could give you some 'dirty' filter material which you could put in your filter or tank to help seed your filter? Your cycling needs a kick start.
If you do lose your fish, and I hope you don't, then consider cycling the tank without fish and only add fish when your tank is ready.
Best of luck.