No air stone, not measuring your ph and not knowing the EC of your nutrient mix puts you at a dis-advantage from the get go.
Pepper plants enjoy a PH of 6 or thereabouts. I measured some rainwater here at home it came in at about 4.7, if your rain water is anything near mine then that is problem number one. Nutrient lockout due to incorrect PH. Plants cannot feed when the water is at an incorrect PH value.
Solution- Buy a liquid test kit from your local pool shop, pet shop, bunnings etc. They are around ten dollars and will last around 6+ months, longer as you get to know your water better and how much PH adjustment it needs.
Adust your water with PH up if it is low (hydroponics shops sell PH up and down, also i found that a brand of rust remover at Bunnings is exactly the same thing, phosphoric acid, and is about 1/8th of the price ($18 a litre vs $11 per 125ml). The only difference is that the proper stuff has 850g/litre and they rust remover has 650g/litre). Or if it is high adjust it down with PH up. Such a smalll amount of the chemical is used that these bottles will last for years. To adjust my 50 litre res from 7.5 to 6 uses around .5ml so this bottle should last me 250 water changes, about 4.5 cents per change. A small syringe comes in very handy when working with such small amounts of chemical.
After you have your PH correct you should check that your nutrient solution is at an acceptable level. This can vary wildy from plant to plant, system to system etc so you have to find out what works for you. I just received a new EC meter yesterday after my old one broke ages ago. They are not cheap (well you can get cheap ones but i wouldn't trust them), i paid around $120 delivered from fleabay but they should last near forever and mine came with a 5 year warranty.
I have been using Canna classic at the rate of 1ml per litre as per the guys advice at the hydro shop, without a meter i figured this the safest way to go. After testing the EC i found that it was 0.4 where i wanted to run at about 1.2 for a while and see how the plants responded. If they handle that no worries i will bump it up another .2 and so on. Canna recommends that the product is used between 1.2 and 2.0.
Now, if you haven't got the spare cash to throwing on an EC meter i wouldn't worry all that much. There is a very simple way to tell if you have too much food in there, the tips of the leaves will burn. Keep track of how much you feed them and when this point is reached reduce the amount of nutrients (you running half strength there shouldn't be a problem though). Also, get that air-pump and stone, other wise you will have to replace the water very often.
Really what you need to do as soon as possible is to nail that PH. It is the most important factor and if it is out too much your plants will refuse to grow and they may actually get together and plot your murder.