Sorry to hear you're getting this.
In the Adobe Crash Reporter dialog can type in your e-mail address and send the crash data to Adobe.
Have you done that?
Have you checked if your computer meets the system requirements for After Effects CS4? (listed in the documents I linked to).
If you just upgraded to CS4, you can call the Adobe Support team as your licence allows you several phone calls to the support, including for installation problem.
Thank you Sébastien, but they were of no help.
Then I was tipped off that I would probably get better help here.
I have a feeling the tip might be right.
Going to check out the troubleshoot link Adolfo left above.
If I'm able to figure this out on my own, I will come back here and leave a post.
For now, my problem has not been answered... yet.
Could you try this:
Run the CS4 clean scripts.
Uninstall every CS4 products you have.
Uninstall Adobe Air and any Adobe Air app.
Uninstall Adobe acrobat reader if it's version 9 or above.
Uninstall any plugins you have installed in CS4.
Update all your drivers, and your Windows/MacOS
reboot and try reinstalling AE CS4.
Does it work ?
Do you have Magic Bullet? There's been some major issues with MBL and AE lately. They have one set of fixes for the newest MBL release but the new OS X crashed the computer now.