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

Try to edit the time the User_Feed_Synchronization is set to a different time and see if your machine restarts. This seems to update your RSS feeds.
Does it go back to sleep after the task is finished?

I've looked in Power Management before. I didn't say anything about it because I can't even check the "Allow this device to wake the computer" option, as you can see in the screenshot.

Are you using a wireless mouse? If so look at its power management tab and see if that is the cause.

Yes, I am using one, but I power it off every time I turn the computer off. I found the option and unchecked it. Usually it only works when the laptop is in sleep mode. Sometimes I left it on and the computer didn't turn on. I don't think this will be a solution, but I'll see if it works...

Try this by first entering command prompt, press start button and in the search field type cmd, right click on it and run it as administrator, then type this:

Code:

powercfg -devicequery wake_armed

press Enter. This should gives a list of the devices that cause the pc to wake up. If it shows a device on the list then you need to go to Control panel -->Device manager, find that device and right click on it to open its properties, then go to the power management tab and uncheck Allow this device to wake the computer. Take a snapshot of it so we can see the result.

Do you log in to your pc as an administrator? If not use this artice to enable it. Built-in Administrator Account - Enable or Disable

Have you your phone linked to you computer in any way, like PC Monitor for example or Pocket Cloud?
Those programs are linked to the app on you phone to allowed you to wake pc, send to sleep, switch off, or watch activities and current users - all that kind of stuff. Anyway if you have something like that then it could be the reason why your laptop wakes up. I am sure I had a similar problem - not any more.
Hope it helps.

@mach04 : I've tried the command. It doesn't show any device.
@Kaktussoft : Only hibernate, I don't even leave the laptop in sleep mode over night.
@taraskyn : I don't have any device linked to the laptop besides a wireless mouse.