Pre-comp shows the background color, although the layers are visible

Your screenshots tell us nothing at all about the logo_hand comp except that layer 3 is a nested comp with collapse transformations turned on and the rest of the layers are shape layers. None of the layers have effects applied. 

Your 00_symbols comp screenshot tells us little about the problem layer 8 (logo_hand) except that the hand appears to have an oval dark gray background.

The only thing that makes sense to me is that the Background Color of the logo_hand comp is set to white. Background comp colors don't render because there are no pixels in a comp until you put them there. I don't know what is supposed to be showing in the logo_hand comp. It could be that there is a large shape covering everything. Have you tried soloing layers in the problem comp. Have you tried adding a background solid or shape layer? 

I would try troubleshooting by checking all modified properties, make sure comp BG color is set to black so you can see potential problems, and finding the problem layer or layers. If you still can't figure it out embed some screenshots with the modified properties of the problem layers revealed. Just press "uu" and embed a screenshot.

One more suggestion, to make it easier on us: The "Drag & Drop here..." area is buggy and should not be used to share images. Please use the toolbar or just drag your images to the reply field. If you can't see them when you are writing your post it's a pain for us to look at them, especially on mobile devices.

Probably an issue with GPU acceöleration vs. the small initial size of the logo elements vs. continuous rasterization. after all, you are zoomed in 400% which means that the logo is actually rather tiny, which for vector based artwork doesn't even make much sense in the first place. Make the comp and the convertted shape layer elements larger and perhaps it fixes the issue. Otherwise you'd have to drill into the shape layers themselves. Perhaps there's some stray effect or layer style that affects rendering with CR enabled.

Mylenium