NOOB question = Cloudy Water during cycling

Just a simple question... I am cycling a 15 gallon nano tank. For the first
couple of months, I just let it run without anything in it, and then I added
two mollies. But the water never has lost it's whitish,cloudy look to the
water. I have crushed coral for a substrate. Now that I have added 130 watts
of proper Compact Floresent lighting to the tank, there is green algae
growing on the glass and bottom. I was told not to do a water change becaues
I will screw up the cycling process. What do you think is making the water
remain cloudy for these long months?
I don't have all the test kits yet, but I do have a ph and nitrate and
everything seems fine. One thing I have now is babies... the two mollies
have had babies... 15 are still alive. I'm also thinking that I should
remove the babies because that might be putting too much of a bioload on the
cycling tank, they are roughly 1 inch long now.
I have had tanks for years by the way, but all freshwater. I have an 80
gallon, 15 gallon and 1 gallon setup, but this is my first nano tank setup,
so untill I find out what is causing the cloudy water, I don't want to add
any coral yet.
If you have any idea as to what to check/change to remove the
cloudiness from my tank, please reply. thanks in advance.

Caper
Dartmouth, Nova Scotia