Reference File
Dropbox Link to Reference File
Overview
I've included a very, very basic file that creates the structure of a more traditional animation style that is commonly used in Flash with some studios near me. I cannot share the original file because it is copyrighted material. The problem I'm having is the same in both files, though.
I have multiple sets of nested Graphics (not Movie Clips, as I cannot use them). Based on the setup that I'm using (see reference file and General Setup section below), the main timeline will not animate when scrubbing. Additionally, animation does not occur from the nested Graphics when published.
I've spent hours researching the issue to no avail. I'm at my wits end and hoping someone else has the answer. Any insight as to how to correct the issue would be extremely helpful.
I'm hoping others can benefit from the answer that arises here.
File Setup
Main timeline created with one key frame and 30 frames
There is a parent Graphic on the main timeline. Inside the parent Graphic there are four key frames. Each key frame contains a child symbol that is animated.
On the main timeline, I've selected the parent Graphic (Line States). Under its properties, I've set Looping to Single Frame and entered 2 as the first frame.
When I enter Edit Mode for Line States, I select frame 2, and click the child Graphic (Vertical). Under its properties, I've set Looping to Play Once and entered 1 as the first frame.
When I enter Edit Mode for Vertical, a 30 frame shape tween has been created to animate from a straight line to an S-curve.
The Issue
From the main timeline, scrubbing shows no animation. From a published output file (swf, etc.), there is also no animation.
The Request
Please help. 
If anything is unclear, please let me know. I will update with clarifications based on feedback.