Possible Duplicate:
Can we develop a game for iPhone on Windows platform?
Are there any available game engines that I could use to develop on Windows instead of on Mac?
I'm aware there is XCode for Mac, but I'm looking at a game engine for iOS on Windows.
I'm open to paid or free engines, but mainly free ones (to keep my operating cost low, unless that paid engine is really, really good)
Look into Unity. It's free to develop with for PC/Web, so you can develop your entire game, test it, and then port it to iOS with little effort. The iOS exporter is $400.
Whichever route you go, though, I think you'll probably still need access to a Mac to actually compile your app for iOS.
This question: (which may be a duplicate) may also be useful to you.
Notes:
It seems you are confusing the terms "IDE" and "game engine." XCode helps you write code; it's an IDE. A game engine, on the other hand, provides a framework for your code to run in once you've written it. Unity encompasses both: it includes an IDE and a game engine.
Corona is a very good tool for developing 2D mobile games; you can develop for Android on Windows and then compile to iOS on a Mac.
