My laptop's battery drains when in hibernate mode. How can I troubleshoot / fix?

Shut down the computer, rather than hibernate it.

If it drains after 24 hours, then the fault is a bad battery.

If it does not drain after 24 hours, then it's not really hibernating. The computer is powering up for some reason.

The command powercfg -energy will give a report on power settings and usage. It should show any issues. Take a look at that, looking for the warning messages.

EDIT: The -energy option only applies to Windows 7 I think. I withdraw my answer from your case, but I'll leave it here in case anyone else can use it.

It turns out that the battery drains even when my Sony Vaio Z is switched off (about 10% every 24 hours)

There's a 50 post forum thread on this 'design feature', but no way to fix it:

http://forum.notebookreview.com/showthread.php?t=299109