Sorry to disappoint, but since you are not really saying anything useful (not even what version of AE you are using!) I feel we cannot give you any specific advise other than to "trash the preferences". For everything else we need more info. MediaCore crashes can be anything from bad CoDecs to equally badly configured graphics drivers to problems with the media cache, but we really need to know more about your system. And QT32Server is not relevant here - it is actualyl only launched as an auxilliary process by AE, not before....
My version of After Effects is CS 5.5, the newest version. My system specs are as follows:
Processor: Intel Core 2 CPU 4400 @ 2GHz
Memory (RAM): 4.00
Operating System: 64-Bit
This is the only useful info I found under Control Panel => System.
What else do you need to know? Any more info I would be happy to provide.
Also, even though I have never opened it (and therefore never changed/saved the preferences), would deleting the preferences still help?