G5 shutting down
My G5 recently developed a problem where it boots up and then shuts down suddenly and completely within a minute or two.
Answer
I'm guessing that you have an iMac G5. It likely suffers from a failed logic board, power supply, or both.
Apple recognized this defect in manufacturing and offered a 'repair extension program' to fix these machines. Generally, your machine must be within 3 years of the date of purchase in order to be fixed by Apple for free.
More information about this repair program is available at http://support.apple.com/kb/HT2390