One thing you could try is a complete clean installation for your CS6, by first running the Adobe Creative Cloud Cleaner tool on your system. Note that this also supports CS6 removal.
It's a drastic step but might do the trick - Make sure you have your serial number and installer disks handy before you run this so that you can re-install your software.
Then follow the steps from the following Adobe Support Page:
What OS do you have?
Did you update your OS recently?
Did you buy a new computer? Whan Yes, how did you install the program? From migration or backup disk or from the installer?
did you try the Creative Cloud recently?
That process may have hijacked your orderly licensed version of InDesign CS6.
Your 30 days of trial could be over now and so CS6 would also reject to run.
I observed, that the serial number of a perpetual licensed and installed InDesign CS6 has changed after installing Creative Cloud.
Note for a little bit different scenario:
If someone is changing from CS6 perpetual to a paid version of CC and already was using paid 3rd-party plugins with the perpetual licensed version. The plugins will not run after installing CC, because the serial number of CS6 has changed.