Greetings Carl,
Yes, a Muslim must believe in all the books revealed by Allah, namely the tauraat, zaboor, injeel and Qur'an.
We believe that they were books revealed by Allah to the respective Prophets. None of them now exist in their original form. So we believe that Allah originally revealed them, and they were originally 100% Allah's word, but people changed them, thus we do not follow them, and only follow the final and unchanged revelation, the Qur'an. Allah Himself tells us in the Qur'an that people changed them, and He says of those who did:
Therefore woe be unto those who write the Scripture with their hands and then say, "This is from Allah," that they may purchase a small gain therewith. Woe unto them for that their hands have written, and woe unto them for that they earn thereby. (2:79)
Please note that the injeel does not equate to the New Testament found today, which is largely written by human authors. The original injeel was the word of God, given to Prophet Jesus (peace be upon him).
Allah never made Jesus as God in Christianity, God was always Allah alone, but people changed the injeel and mixed up human words into it, and they elevated the status of Jesus (peace be upon him) to divine. Prophet Jesus (peace be upon him) always told people to worship Allah alone.
This is a quote from a different post:
Islam is the only non-Christian religion which makes it an article of faith to believe in the central figure of Christianity, i.e. Jesus Christ (peace be upon him). If a person calls himself a Muslim and doesn't believe in, respect, or love Jesus (peace be upon him) then he is NOT a Muslim. No other non-Christian faith has this stipulation.
We believe that Jesus (peace be upon him) was one of the mightiest messengers of God.
We believe that he was the messiah, translated as christ.
We believe he was born miraculously without any male intervention, which many modern day Christians today do not believe.
We believe that he gave life to the dead with Gods permission.
We believe he healed those born blind and lepers with Gods permission
However we do not believe that Jesus (peace be upon him) ever claimed divinity, or that he was God, son of God, or that he said "Worship me". We also do not believe that he was crucified, nor died for anyones' sins. In Islam, each person is accountable for their sins.
We believe in One God, who has no associates whatsoever in His Divinity, and we believe in all the prophets that He sent to mankind, whether we have heard of them or not. That includes the final Prophet Muhammad (peace be upon him). We are not allowed to pick and choose those we believe in. We also believe in the existence of all the books of God i.e. Bible, Torah, Psalms of David (peace be upon him), and any other books that we have not been told about, revealed before our time. We also believe in the angels, and Day of Judgement.
Peace.