The people you speak of who love their neighbor by caring for the sick, the elderly and others, who you say never received Jesus and will thus be in Hell, are they whom the Lord refers to as His sheep in Matthew 25:33-40, who thought they did not know Jesus. They know love, and love knows them.
To believe ON Jesus is to believe IN Jesus, both of which mean to believe IN/ON what Jesus IS, which is Love. Remember there are going to be many at the judgment seat who are going to say to Jesus: "Lord Lord...", supposing they believed IN Jesus, to whom He/Love will say that He/Love never knew them.