G'day Mate,
Good on you for keeping up the effort.
'Choempi' is right, you have powdery mildew there, at the same time though you are doing the right thing with the Neem, however I don't think you should be using it every day as it may 'suffocate' the plant (as described in other threads). Use it on alternating days but there are other things to do...improve air circulation, address humidity, and trim affected leaves, like cut them off but not too much all at once. Some of the more experienced growers used sulpher but I think that is a little over-kill for your one plant in the set-up you have. Sadly as it gets to your buds they will stunt so work on giving the bud sites the best TLC first.
It's a bit late now (maybe) but I think your lights are insufficient, I grew with CFLs also but I had a hell of alot more than four 20watt CFLs.
I note that you've addressed the perlite issue, another tip is this..if you use a medium that already has nutes in it but then you realise that the plant is deficient in something (like your nitrogen), then try foliar feeding instead of adding more to the medium.
In my experience I had to supplement Cal/Mag (due to excessive peat moss in the medium affecting the Ph) so I foliar fed with Epsom Salts while I addressed the soil Ph. In your case you may have gone with say foliar feeding with Orchid food which is very high in Nitrogen, that way you could maintain control of how much N it received whilst flushing the soil to address the Ph or lock-out.
Good on you for keeping it up though, we all have to start from the beginning right? You're persistence is going to reward you soon enough.
And if anyone asks about the "new plants" tell them it's a new Brazilian Tomato plant that you're trying out.
One Love,
Yarndi.