His video card has nothing to do with hibernation, dude.
When a computer goes into hibernation, it takes the current state of the system, saves it to the hard-drive, then kicks off. When you turn the box back on, it has instructions leftover from the hibernation that tell the computer to restore from the hard-drive, and away you go again.
What OS are you using, Amit? If it's XP, you have to enable hibernation in the power settings in the hibernation tab. There may also be a physical limitation, such as not having enough hard-drive space for the hibernation.
In Windows 2000 and Windows XP, STANDBY and HIBERNATE are supported and can be activated on the OS level. For Windows 98, it has to be a feature supported by the manufactuer of the PC.
Although STANDBY and HIBERNATE both perform power-saving functions, they are different in behavior.
STANDBY cuts power to peripheral devices when they are not in use, including the monitor and hard drive. Power however is left on for RAM so whatever's in physical memory won't be lost, e.g., any work that you may have done remains before STANDBY sets in.
HIBERNATE saves the contents of RAM to your hard disk when you turn your computer off. When you switch on your computer again, documents and application are open just as you left them before the powering down.