This may be completely unrelated, but I had the same problem and it stayed that way for about a week. I upgraded quicktime to the current version and then After Effects worked perfectly. You might want to try that to see if it helps.
Seems like it should be really straighforward to update QT, but the App Store says no updates available. Did you get it manually somhow?
This is a fairly common issue when upgrading to Mavericks, or really anytime that you upgrade an existing operating system instead of using a clean install of the OS. I would suggest repairing disk permissions as a first step. Here is a website with instructions - http://macs.about.com/od/applications/ss/firstaid_3.htm
If this doesn't help, you may want to contact our 1-to-1 support team. They can help with this issue much easier than going through these forums.
Thanks Greg. I actually did go through disk utility and repair permissions, but I'll try again. How do I get in touch with the 1-1 help?
It seems that you have some third party plugins installed on your machine. Please navigate to the below location and remove all the plug-ins from Media core folder and then try to launch the product.
MAC HD or Startup drive/Library/Application Support/Adobe/Common/Plug-ins/7.0/Mediacore
I have a Matrox mx02 installed. Removed those drivers and it opened up perfectly.
I will get the updated drivers from Matrox.