Can a windows 7 computer turn on by its self

Can a windows 7 computer turn on by its self connect to a wifi internet connection start itunes and go to a specific radio station play for a few hours and then turn off and be able to do it all again night after night?
I have a friend and she just can’t get how to use a computer no matter how I try and teach her. She has a wifi connection and would like to listen to a specific radio station at night while she falls asleep. At present she listens to a station via itunes when I come to visit and I get the station for her.
I wonder can a computer that is off be made to boot or does it have to be in hibernation or stand by to come on and where in windows 7 do I make the settings as to what time of day to come alive or on from being off. And I assume the same place is where I will have to put in settings to power off or go into stand by or hibernation. So first off is this possible?
I am a Mac guy so not sure but I think I already know where and how to tell it if a particular wifi is present to connect with it also if it loses the connection will it automatically reacquire that network?
If the above is possible can I get itunes or Internet explorer or firerfox or other internet browser to startup and go and connect to a radio stations live feed via wifi without having to manually click on any button on the page?
Is what I want to do very complicated and could be prone to hang or freeze and she would have to be computer savvy to get it all going again which like I said above she is not. Could she just hold down the laptops power button shut down and then repress to restart and it would come back on and all would be able to pick up where it left off?
Do I approach this as have itunes always running connected to the station could the computer be made to go to standby or hibernation at a specific time and itunes would continue to run just not make noise so when it comes out of stand by or hibernation it will be on and connected streaming the radio stations music?

You can do all the above by creating scheduled Windows tasks. The only thing you can't do with Windows is have the computer turn back on. This you can do from the BIOS in the power management tools. There should be some setting like "Auto power up" or "Resume by alarm" or something like that. (each BIOS will be different). To get onto you BIOS restart your computer and press delete when you get to the screen that says "Press DEL to enter SETUP" (or F12, or whatever it says to press to get into BIOS).

To learn about scheduling tasks look here:
Task Scheduler - Create New Task - Windows 7 Forums

or here:
Schedule a task