It looks like I'm going to be a regular here
The computer won't hibernate. It takes its time then shuts down. However when I resume Windows, I get the "Start Windows normally" screen and surely everything was left open would be lost. Same goes for hybrid sleep, but I'm new to that since I just converted to Win7 recently.
I used to have this problem when I was using WinXP but with a slight deference: the computer used to get stuck on the blue screen and never shuts down. Therefore I'd have to cut off the power myself.