The change in your heart is God's part, and He will attend to that. Your part is simply to believe and trust in Him to attend to whatever is necessary for your eternal salvation. To receive Gods free gift of eternal life and righteousness all you need to do is simply put your trust in the Lord Jesus. You need to trust in the work Christ has already done. Simply believing that there is a God or that there is a Saviour, is not enough.
Devils believe that and tremble.
Jesus died for all our sins, salvation is bought for every man in the world, if he will have it, as the free gift of God. The change of heart is not a matter of feeling. Some do not want to claim Christ as Saviour until they have the mysterious feeling that they want. The Bible nowhere tells us how we must feel before we are saved, or after we are saved. All people do not feel the same, feelings vary with the each individual person saved.