I have a Sony VAIO where the 'sleep' key ('zzzz') is a function key sharing F12. When I use it, Windows hibernates instead of sleeps. Windows is set for sleep to be enabled and it works with I used the start menu and when it hits the sleep time on battery mode, but the key doesn't work and I can't see how to map it correctly.
Ensure you have the proper "Setting Utility Series" and "VAIO Control Center" utilities for your OS/Vaio model installed and then use the Control Center to reassign the key.
You should be able to get these utilities from your Vaio's support page.