It says from the picture my computer does not support hibernation. But sleep mode is just fine when I put it in sleep mode. Though I can't wake up my computer through pressing the mouse or keyboard. I have to press the power up button on the pc to wake it up. I checked Win7's power settings and everything is fine. I just saw a recent thread in the forum about hibernation problem but his is not the same as mine.
Hibernation is different, that writes the contents of the RAM into the hard drive, and shuts off the computer. When you turn it on, the settings come back like they were when you turned off the PC. Sleep just puts the computer in low power mode but does not shut it off.
If you are using an active desktop (web page, active content) for your background, it will not hibernate. Your post is a bit misleading as you say you have an issue with sleep mode, the issue is with hibernation. Change your background to a regular picture or no background and try hibernation after that. You may need to install some more drivers for your computer if you still have issues after changing your background picture.