Did it ever work? Is your default printer network or local, and is it turned on?
If you create a new user, does it work when you log in using the new account?
Unfortunately windows doesn't provide useful crash logging for ID, so we need to guess. My memory is that this used to be caused by SING ( see SING Removal) but SING was removed from CS6, supposedly though maybe the plugins are stil there for use with legacy files. It can also be casued by bad prefs ( see Replace Your Preferences) or a bad font (Troubleshoot font problems | Windows) in addition to the account and printer problems mentioned above.
You'll find a lot of threads about this if you google site:forums.adobe.com "starting up service registry" InDesign
How did you verify that the problem is in CoolType.dll?
Do you use a font manager?
Trying a brand new user is a very important diagnostic step. It distinguishes betweeen general problems (system or application) and problems isolated to a particular user account. That makes fixing the problem a lot easier.
I dont have a font manager and this is the report after crash:
Nome evento problema: APPCRASH
Nome applicazione: InDesign.exe
Versione applicazione: 184.108.40.2066
Timestamp applicazione: 50335e39
Nome modulo con errori: CoolType.dll
Versione modulo con errori: 220.127.116.1154
Timestamp modulo con errori: 4f207049
Codice eccezione: c00000fd
Offset eccezione: 001abfcb
Versione SO: 6.1.7601.2.1.0.256.48
ID impostazioni locali: 1040
Informazioni aggiuntive 1: 6b93
Ulteriori informazioni 2: 6b93c9753c172ff0964886f0a0723489
Ulteriori informazioni 3: d5f4
Ulteriori informazioni 4: d5f4f3abcd96c65338708a751b702029
I suspect that could mean a bad font rather than a corrupt .dll file. Windows reports are not very helpful.
Did you try resetting the prefs?
And have a look at the font troubleshooting link I also posted above.
OK, if it doesn't work in a new user that means it's at the system level somewhere, probably back to either a bad font or a damaged install. If you've done the font trooubleshooting, I think you should probably uninstall, then run the clean tool (CS Cleaner Tool for installation problems | CCM, CS6, CS5.5, CS5, CS4, CS3) and reinstall. Before reinstalling I would recommend running MSConfig and truning off all non-essential startup programs and services, then run it again after the install to restore normal startup.