Macbook (OS X 10.4.11) shutting down w/o warning

I'm trying to help a friend troubleshoot why her old MacBook keeps shutting down without warning within minutes unless she is actively typing or using the touchpad. The 56 GB hard drive is only 1/2 full. Since she only does email, Netflix and an occasional internet search, she would like to avoid springing for a new computer. The battery is fully charged and we already tried a different (newer) power supply. Does this sound like a motherboard issue (in which case she's better off just buying a new laptop) or could there be a virus or malware that does this?

Thanks for any help whatsoever!