The CMOS battery is mounted on the motherboard and you should be able to remove it from it. Four years is a long life span for that battery. If the battery is bad it won't keep your setting in the BIOS, if it is bad the date and time will not be accurate.
Have you tried getting into safe mode? If you can get into safe mode look in the event viewer and see what is showing up when it is shutting down.
What happens if you right click in the tool bar, does it shut down the computer as well? When the computer shuts down are there any LEDs or is it completely dead?
If you have a voltmeter see what the output of your power supply is.