For troubleshooting, I would agree with the other posts.  If you have spare parts. start swapping them out one at a time and see if the problem persist.  Start with the CD/DVD just in case the unit is malfunctioning.  Next borrow a power supply from someone and swap that. 

In most case, fan failure will be detected by the motherboard and you will not be allowed to boot beyond your bios.  As a last resort, check your RAM.  I had an issue with one computer where it would shut down without warning and in order to reboot, I had to unplug and replug the power supply.  After changing video card, fans,  power supply from spare parts and eventually resurrecting a spare motherboard into a new case, did I find out that 1 DDR chip had gone bad.  That took me a better part of a year to figure out.