Does that behave occur when on battery power only or with mains as well? If it isn;t a power issue, the RAM (memory) might be flawed or the hard disk might be failing. Do you hear any sounds from within?
If you don't hear anything, the fan has stopped and the system is closing down to protect itself. If you can hear the fan but also a sort of grinding sounds, it may be the hard disk. If that is the case, don't switch on again. You may still have a chance of retrieving your data.
More on that if you need it.