The "Power button" in Windows 7 is the one shown in my picture. If you click start and then the small arrow beside the "shut down" text, you should see it. But are you saying that the hibernate feature is not in that drop down menu?
Attachment 659
The "Notification area", as you are probably aware, is the area to the extreme right of the taskbar.
If you click the small arrow there, and then "Customise", you will be able to alter the visibility of several items. Power is one of them. But you cannot selelect hibernate through this icon, only through the "Power button".
If the hibernate option is not showing, do this:
1. Open a Command Prompt. (its in the Start menu - you should right click it and "run as Administrator"
2. Type
powercfg -h on and press Enter.
You should now be able to set your Power Plan settings to the recommended settings for Hibernate