... That was a little backwards. It's not that God gets farther away from us when we sin, it's that WE get farther away from God. We're the ones that become allergic to God when we sin.
Yes, it means we don't die anymore! I keep forgetting, everyone that is non-religious thinks of dying as so physical. Death to me is a very metaphorical thing. When our physical bodies stop working then we go on to Heaven to bigger and better things, where our true lives just begin.
Before Jesus we couldn't go to Heaven because sin (using my previous analogy) made us allergic to God and Heaven's Holiness. But Jesus conquered and beat down sin for all of us, so we just ask Jesus to take away our sin and then that cures our allergy so we can have fun in Heaven when we die. Jesus is like Clarinex without a prescription... (boy, I can see that quote coming back to get me later on
)