Acts 24:14-15 (NKJV)
But this I confess to you, that according to the Way which they call a sect, so I worship the God of my fathers, believing all things which are written in the Law and in the Prophets. I have hope in God, which they themselves also accept, that there will be a resurrection of the dead, both of the just and the unjust.
Paul had to defend himself in front of Governor Felix against the trumped up charges made by the Jews. He speaks of the Way, worshiping God, the Law, the Prophets, and the resurrection. That's quite a list of spiritual topics that Paul is able to touch upon in the secular setting of a courtroom. Note the emphasis on the resurrection, particularly that it is for "both of the just and the unjust." It is a shock to realize that we must all spend eternity somewhere. I've heard my pastor say, "You can't crawl up in the grave and pull the dirt over your face and hide from God." This must have had an impact on Felix because notice what happens later...
Acts 24:24-25 (NKJV)
And after some days, when Felix came with his wife Drusilla, who was Jewish, he sent for Paul and heard him concerning the faith in Christ. Now as he reasoned about righteousness, self-control, and the judgment to come, Felix was afraid and answered, "Go away for now; when I have a convenient time I will call for you."
Can you imagine having a private hearing from the greatest preacher of the grace of God that the world has ever known? As shaken as Felix was, he could not let go of his ways and decided to put the decision off to a more "convenient" time. That time never came for Felix.
2 Corinthians 6:2b (NKJV)
Behold, now is the accepted time; behold, now is the day of salvation.