I have a feeling you do not know exactly whether you are asleep or hibernating. One way to find out is how you wake up. If you can wake up by hitting any key, then you are asleep. The power key is the only one that wakes you up from hibernation (just like turning on from shut down). To have better grasp of how your pc behaves (sleep and wake up) and what to do when it is misbehavin', program your power plan.
Double click the power icon at the notification area of taskbar then double click MORE POWER OPTIONS. From here instructions are easy and self explanatory.
When done, you're in command.
PS...In case you have no icon for power option in taskbar, you can go to control panel and hit POWER OPTIONS. BTW, it is nice to have an icon there so you would know whether you are plugged in or on battery.