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If you boot into Safe mode, do you still have the same problem? If not, then it might be due to some login item that is launched when you first log into a user account.
I looked through the list and found base installers for all OS versions up to 10.6. However, like you, I could not find base installers for 10.7 and later. I'm guessing that is because starting with 10.7, the OS was only available via the App store. Unfortunately, that means that you'll only be able to get the installer from the App store, and the only way I know of getting older version from the App store is if you have previously "purchased" that version and wish to download it again.