What files would those be? Are you referring to the prefs? See Access hidden user library files | Mac OS 10.7 and later and Replace Your Preferences
Running in an alternate account suggests a permissions problem. See Cant launch new inDesign CC | Adobe Community (but use Version 8.0 for folder names), and Adobe Forums: InDesign crashes at startup or you can try just deleting the two preference folders from the user that doesn't work and copying them from the user that does.
Actually, blowing away the prefs was the very first thing that I did. That didn't help.
And then I completely uninstalled, and re-installed the program twice. That didn't help.
On your recommendation, Peter, I just did it again. Prefs do not seem to be the problem.
In my particular case, inDesign does not crash on launch, but as the welcome window shows up, it takes about two minutes to be usable. Attempting to click anything results in the dreaded beach ball.
Once in the program, sometimes it behaves, other times it is unresponsive.
I deeply suspect a Suitcase/Flash connection. The Extensis Font Pane uses Flash, but I no longer have Flash on my system. I do not use that pane, as it is exceedingly slow (I have a lot of fonts). I re-installed Flash, just to see if that was the problem, but that didn't help either. Then I removed the Extensis Font Activation pane. None of those desperate measures hve helped.
You must have an old version of Suitcase Fusion. They no longer use Flash for their panels.
BTW, what version of OSX are you running? Was it a clean install? In place upgrade?
I have the latest version of Suitcase.
But if they're no longer using Flash, that would explain why re-installing Flash made no difference,
Back to the drawing board.
I am using Mavericks 10.9.5.
BTW, I did not reinstall the OS. I did re-install inDesign. Twice.