after today it's going on an embarrassing 20 hours of trying to solve this. Most of which was with Adobe tech support.
tried the solution from 1611kjb which initItaly worked for 3 successful launches of AE, but got a trial expired notice! So I logged out of CC, restarted the machine and launched AE (after having renamed the exportavi file)... after effects was resumed its "initializing media core".
tired, missing a deadline, I just need this to work. re-uninstalling-installing/ regedit mods aren't helping.
What version of AE are you using? If it's CC 2015 (and updating to the 13.7 version that just launched late yesterday doesn't work), try running CC 2014.
thank you Szalam,
this was a fresh install of AE which started with 13.6 and ended today with 13.7. performed some of the same steps as before and it looks like it's either a corrupt user profile or something with the OS. Created another user profile and it AE now launches!
Glad you got it working! Thanks for sharing your solution.