First, by "almost starved herself the other day", I assume you meant she went a day without eating. I could be wrong, but most people over feed their pets anyway and if something like a change in diet causes them not to eat for 24hrs, they break down and give in. My grandmother was a prime example. She kept up to three different brands of dog food in the house and if the dog went a day without finishing entire bowl of food, she said she was tired of it and switched her. However, she was feeding her a loaf of bread and 2 packs of sliced ham a week, the dog didn't need the dry food and to be honest we'd probably eat pizza all week and not eat a balance meal if we had the choice.
We got her, she'd try to snub her bowl of food and treats we gave her, because she was used to being in a single dog household and her treats being there when she deigned to eat them hours later. There were two hover vacs at our house, however, and the food didn't last 20min, much less hours. It took her about 2 days to learn to dive in and eat when I put it out.
Secondly, from wet to dry is a huge dietary change and cats make a change from dry to wet, much better than the other way around. If you don't change the diet gradually, you can expect an upset stomach, for up to a month from what I've heard, but usually less. Boiled chicken is an excellent treat or additive, but not a balanced meal. It takes a lot of work to come up with a properly balanced diet and the pet food companies put a lot of money into testing their products and balancing everything down to the amino acids. As much fuss gets made of gluten and where a product was produced, chances are they will be more balanced in the long run than a food you make at home. Though, with a vets help, you can develop meals you prepare like you would your own that are pretty well balance. She probably doesn't want to go back to the chicken because the taste of the wet food was more complex, and she was probably also getting things she was craving due to possible deficiencies.
I'm not saying you're doing anything wrong, but if it was me, I'd do a little research and find an affordable, quality wet food and keep her on that. People like to mix up their pets foods to give them variety, like we crave, but with most animals a change in diet actually upsets their stomach and makes them sick. They'd much prefer a routine of the same diet on a regular basis. Also, I was reading an article recently about how cats don't naturally drink very much from standing water. The definitely will and you should always provide fresh water for your cat, but the article was saying that they typically intake more water than you'd expect from their food and lack of water in dry foods contributes to bladder crystals. Good luck with your cat.