Hi Stuart,
Yes, the battery can die at any time but there is normally an associated message to the effect that “no battery is detected”.
Try opening Control Panel > Device Manager and expand ‘Batteries’. Right click each device and select ‘Uninstall’ – then shut down and re-boot. Drivers will be re-installed on boot.
This should hopefully rule out a software/driver problem. Otherwise I would suspect a hardware issue.
You could also try shutting down, remove battery and power adaptor and hold down the power switch for up to 30 seconds. Re-attach battery and power adaptor and re-boot.
Ultimately try a reset to factory defaults using Vaio Recovery Utility – last resort obviously...
Rich