I've heard mixed thoughts on cycling products, it won't hurt your tank though. Neons can be very fragile fish so I wouldn't be too suprised if they die in a brand new tank unfortunately. Do you have a test kit? If you don't, go out and buy yourself one of the liquid test kits for pH, ammonia, nitrite and nitrate (and read up on the nitrogen cycle so that you can interperet the results!) API makes a nice freshwater master kit. If you see a spike in ammonia or nitrites, your cycle isn't doing its job and you'll want to monitor your tank closely and do frequent water changes. Also, make sure you aren't feeding your fish too much while your tank cycles and don't add any more fish until you've got consistent readings of zero for ammonia and nitrites.
Since you just started your tank, your neons are probably stressed by their new environment, you could try a bit of frozen bloodworm or brine shrimp or freeze dried treat foods if they absolutely refuse to eat (remember to only feed a little!) Make sure that you continue to give them a bit of flake food as well since it's more nutritious than just treat foods.
Once your tank is cycled and you want to add new fish, make sure that you research new additions and plan out exactly what you want in your tank before you go fish shopping. It's very easy to make stocking mistakes in a tank that small, but you will have a lovely tank if you get it set up with the right fish, so far you're off to a good start!
Good luck on your new tank!