Your board won't stay in Sleep because something is waking it up (duh, I know... ) One of the usual causes is USB devices. In Windows Power plan option, select your plan and then click Advanced Option. Find USB in the list and make sure that Selective Suspend is Enabled. You should also check your BIOS to see if you have WOL (Wake On Lan) enabled, since when in Sleep or even Shutdown, the network chip is awake. Even with no Internet activity, the network still "talks" to the network chip.
If you get Sleep to work, you may next find that waking from Sleep fails. That is common with Intel 6 series chipsets like the P67. My ASUS P67 board refuses to wake from Sleep any longer than about half an hour, a strange issue I've never fixed. Some say it is power supply related, or a bug in the P67 chipset.
For Hibernate, which is enabled in Windows by default (but can be shut off manually), look in your BIOS for a Deep Sleep setting, or something that you can set to "S4" which is Hibernate. Sleep is S3. When you click the Shutdown options, where Sleep and Logoff is, you should also see Hibernate. Not certain if you won't see it until S4 is enabled, since I don't use Hibernate. You may find an entry for Hibernate in the advanced Power options I mentioned above.
Hibernate takes the current OS/Desktop state that Sleep stores in RAM, and instead writes it to disk. If you use a SSD for you OS drive, you may not want all those writes on it, which really is not an issue for SSDs anymore.