The Bible makes it crystal clear that a person can only be saved if he/she believes that Jesus Christ ROSE from the dead. The fact that Jesus rose from the dead demonstrates that His sacrificial death was acceptable to God, the Father. If Jesus had not risen, we would all still be dead in our sins – the resurrection was proof that the debt of sin had been paid is full and accepted by God.
Moreover, brethren, I declare unto you the gospel which I preached unto you, which also ye have received, and wherein ye stand; By which also ye are saved, if ye keep in memory what I preached unto you, unless ye have believed in vain. For I delivered unto you first of all that which I also received, how that Christ died for our sins according to the scriptures; And that he was buried, and that he rose again the third day according to the scriptures: And that he was seen of Cephas, then of the twelve: After that, he was seen of above five hundred brethren at once; of whom the greater part remain unto this present, but some are fallen asleep. After that, he was seen of James; then of all the apostles. And last of all he was seen of me also, as of one born out of due time. (1 Corinthians 15:1-8, emphasis added)
The historical accuracy of the accounts surrounding Jesus’ resurrection are often scoffed at by “experts” – this excellent article lists 23 reasons for the historical validity of the resurrection of Jesus Christ.