J.W.
I am from Michigan and I attend a Church of Christ. THe best way I can describe it is we are a New Testament church that goes "back to basics" and worships the way described in the bible. No bands or things to take away from the purpose of going to church, which is to praise and learn about God. It is considered Non-denominational because there is only supposed to be one "type" of church, that is the type that is outlined in the bible.
I would caution you that many churches use the term "non-denominational" as a license to make up their own "rules". Just, please, be sure that the church you chose really does follow the bible. I was once told that if a preacher goes through an entire sermon without multiple references to the bible then he is often stating his opinion on things, not preaching about what God intended for us to know and do.
I am sorry that you felt "burned" by your previous church, but I am glad that you have not allowed that to turn you away from God. Many people have a hard time seeing the difference :)
If you have any questions, please feel free to write back. I will do my best to answer them for you, or find someone who can!