I was exactly where you are for a majority of my life, my brother passed away when I was 14 and it didn't lead me anywhere good, only further from God. I was saved when I was 19 by accepting those steps outlined in faith, and praying that prayer. I didn't intellectually accept them as you suggest, I didn't say "that makes sense to me", I just simply took it on faith, and prayed that prayer to Jesus, asking to be saved.

"Trust in the Lord with all thine heart; and lean not unto thine own understanding. In all thy ways acknowledge him, and he shall direct thy paths." - Proverbs 3:5-6

By praying that prayer earnestly in your heart you commit your soul to Jesus, it's just like the thief next to Jesus on the cross:

"And he said unto Jesus, Lord, remember me when thou comest into thy kingdom. And Jesus said unto him, Verily I say unto thee, To day shalt thou be with me in paradise." - Luke 23:42-43 KJV

And I know it's hard to recognize your sin, and believe in the penalty for sin, without first believing in Jesus. Maybe I shouldn't put them into steps, because it's something that happens all at once. By accepting Jesus you accept the truth of God's word in the Bible, because Jesus is "the word made flesh".

"In the beginning was the Word, and the Word was with God, and the Word was God." - John 1:1

I can tell from your paragraph that you are not incapable of believing, so I will pray earnestly for your salvation.