Immediately after launching or is some stuff loading? You can see this in the startup screen.
If immediately: check if the preferences file can be read and written (privileges).
You could also try and rebuild the prefs file: press Shift+Cmd+Alt when launching
What the crash log suggests? Can you share that. If no crash reporter is getting displayed and AI is crashing on the launching screen itself than can you share the Illustrator logs from console (Applications >> Utilities >> Console).