the folder means it is unable to boot from the hard drive, generally from what you said, freezing and then shutting off. it experiences an error and cannot boot. sometimes it will boot back up but it needs to be repaired.
disk warrior is a good tool that should fix the problem in most cases.
if not you might want to just backup the drive and then reformat it because this is a sure way to fix the issue
programs like super duper will do a complete copy of you system.