Hi Fbndsprz,
Welcome to Sony Community!
Whenever a computer goes off when the power cord is unplugged, this could be a battery that needs to be replaced. Kindly verify that the battery is still working.
Do some troubleshooting for the battery as well to diagnose what causes the problem. For further assistance regarding your product, we highly recommend visiting our Sony Global Web site for information on contacting the Sony Support Center in your region at http://www.sony.net/SonyInfo/Support/.
Regards,
Jen
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