I have imported Illustrator layers into AE many times before... so I know how to do it. I'm not sure why this is happening.
Without details and more than just a screenshot of a black comp window we have no idea what could possibly go wrong.
The first thing that comes to mind is that your AE and your AI may not be up to date. The second thing is that you just need to reboot. The last thing that could be the problem is that you did something unusual in AI that caused the problem.
To diagnose the problem start by importing as merged layers and see what you get. If that does not work then open up the AI file and start by copying 2 or 3 layers to a new document and see what happens there. If that doesn't work just draw a circle and a square on two layers and see if they will import as a comp.
In the future, when you are having problems with a comp or a layer in the comp select the comp in the Project panel so we can see the comp settings. Then select the layer that is giving you problems in the Timeline and press the U key twice to reveal all modified properties for that layer. If there are effects applied try turning them off one at a time. To make sure that something is not wrong with your comp panel try adding a solid to see if that shows up. If you can't figure things out then send us a screenshot of the entire App and give us workflow details. That's the only way to get really good help on a problem that isn't a common rookie mistake.
The issue was simply that I had forgotten to check off "export as pdf compatible file" when I saved. Cheers