In safe mode the computer is booted with a reduced set of drivers and no login items. Given that the problem occurred with a new account, it clearly wasn't your account's login items.
Your next step is either a visit to the Apple Store or (after backing up the computer) wiping the drive and reinstalling the operating system. If the problem is something you've installed or something corrupted you don't want to return it to your computer so I'd avoid restoring from a backup or migrating applications. It should be safe to migrate your account though.
To avoid wasting time, I'd suggest just reinstalling the OS and then playing with the computer for a while. If it seems okay use Migration Assistant to migrate your data and then manually reinstall your software.