It sounds to me like the program may be having a problem creating the preference files. If you go to Replace Your Preferences you find the paths to the prefs listed and you can check to see if the folders are there and if anything is in them. Be sure you turn on visibility for hidden and system files in Explorer.
Since this is the trial, I don't think you can run the cleaner tool and reinstall, but you could try making a new user in Win7 (Control Panel > Users), then log in with that new user and see if ID will launch. If it does, delete the InDesign folders in your original User profile (Not in program files), and copy the ones from the new user. It's also possible just deleting those two folders in your original user and restarting ID will work.
The other thing to check is to be sure you have a default printer online as a local printer, not a network printer, the first time ID is launched. You can temporarily set Fax or SPS Writer as the default printer (or Adobe PDF printer, if installed) in Devices and Printers if necessary.
I think I followed all your advice properly and it still does the exact same thing. Instantly closes after opening then asks if I want to continue the trial. Holding CTRL ALT SHIFT does nothing. And I deleted the preferences. I see InDesign Defaults but I don't know if I even have SavedData. I guess I don't because I have yet to use the program and save anything? If I somehow need this file would it be downloadable anywhere?
If you have InDesign Defaults you should have InDesign SavedData as well. If you look closely at the paths in the link you'll see that the SavedData file is in a different folder. It's under the Local folder in the AppData section of the user profile.
Did you try a different user and check on the printer?