Laptop automatically starts-up, even though I don't want it to

@Kaktussoft : I'm absolutely sure that I'm talking about hibernate mode (the one under sleep mode).
@mach04 : I've tried your solution and I attached a screenshot with the result. As you can see, most of them are VAIO-related.
@gregrocker : 1) It isn't sleep mode.
2) The feed doesn't appear in the Task Scheduler anymore.
3) The automatic updates are off, but I still update my Windows, so it is up-to-date.
4) This whole problem is revolving around the hibernate mode problem... When I shut down, the laptop doesn't turn on, but when it's in hibernate mode, it does. (if you find it useful, on battery is set to 60 min, and plugged is set to 360 min)
And 5) That's why I hibernate rather than shutting down.

There are a lot of VAIO related programs running, and it might be the reason that you are facing this wake up with your pc. One other thing you can do is right click on each and choose Jump to entry and deactivate them one by one and see if the wake up still persists.
There are a set of rules under the conditions tab that might be causing this wake up, you might want to change them.
As gregrocker said you don't need all these bloatware programs to start up with windows, as windows itself has all those settings needed to give a good performance, and it might even give you a faster start up.

The problem is not performance or whether the programs start or not, but the laptop started turning on all of the sudden, without me changing any settings regarding VAIO programs. That is the issue.

This does not happen with a normal Win7 install. It is either hardware-related or has a buggy install we see most commonly with the factory preinstall. But I'm not going to argue with you the differences between having the best possible Win7 install or the worst possible one that you have. Which you want is your decision.

You can go over your Win7 install to look for clues using Troubleshooting Steps for Windows 7