Simptoms:

-Turn Key, acts like no battery is installed (Doesn't even Click)

-Putting Key in while door is open, chime "flickers" or seems accelerated to every other half a second

-Sometimes clicking of what sounds like a Relay coming from under dash on the passanger side. (Found a Box labeled "Free CDC", seems like it comes from there)

I've checked all the fuzes and the battery ground cables... None are blown and the cables seem to be in order. Any thoughts on the cause?

First off, are you sure the battery is at the correct votalge. Second, are you getting power to the starter?

My cavalier did the same thing and it was a cracked terminal