I recently upgraded to Windows 7 and to start with the Hibernate function was missing from the turn off control. I was able to fix that. but when I click on Hibernate the computer slows down for a second or two and then restarts.

This seems to be a common problem from what I have read. I think my problem is with the advanced power settings I have made some changes but they haven't worked.

So if someone who has a working hibernation, would take the trouble to post their settings that I could try I would very obliged.

I have both a desktop & laptop that hibernate properly. The desktop power light remains on & the hard disk light stays steady, but the laptop lights all go off.
I am only posting the settings for my desktop, but the ONLY setting they have in common is: Allow Hybrid Sleep: Off
High Performance
Require a password on wakeup: yes
Turn off hard disk after: never
Desktop background settings, slidehow: available
Wireless Adapter Settings: Power Saving Mode: Maximum Performance
Sleep: after: Never
Allow hybrid sleep: off
hiberate after: never
Allow wake timers: enable
USB settings: selective suspend setting: enabled
Power buttons and lid: power button action: shut down
Sleep button action: setting: sleep
PCI Express: LInk State Power Management: Off
Processor Power Management: Minimum state: 100%; cooling: active; maximum state: 100%
Display: turn off after: 15 min
Multimedia settings: when sharing: prevent idling to sleep; playing video; optimize video quality

I recognize this question asks about hibernation, but I have found the sleep mode to work as well or better when I call it from the shutdown menu. I do have the power settings go to hibernate if I hit the power button, and that seems to function as expected. My Win7 machines are all laptops (and clean installs) so there isn't as much potential for power loss (the battery works) which could make this a different experience for desktop users.

Thinking about likely settings in BIOS, can you give us more machine information (type, manufacturer, MOBO info if you have it ... two apps that may help with this are Speccy from Piriform or Belarc Advisor)?