I was raised a Christian. But I have read the Koran and believe in Allah and His Messenger. Since I also follow the teachings of Jesus, am I still considered a non-believer?
To be Muslim you have to believe in the Shahdah. The Shahdah states that Allah is the one and only true God and Muhammad is in His Messenger.
Muslims too believe in Jesus and call him Isa (AS). Muslims believe that he was a Prophet and a Messenger of Allah and that the Bible was sent to him. The Bible which used today has been changed and therefore not reliable.
If you believe in the Shahadah then you are a Muslim (You have to say the shahadah and declare you belief when you convert) You can follow the teaching of Jesus too. However you have to be careful with the Bible (Old testament and New) as it has been altered and some things go against the teaching of Islam.