That explains a lot!!!
Firstly follow my steps above again to open the hosts file, delete everything you have in yours and replace it with mine by copy and pasting the example one I posted (it's OK, it's the standard one taken from my computer) then close the host file and click yes when requested do you want to save.... you should now be able to access youtube (and all the other sites in the list on yours)
Once that is done I'd very seriously suggest running a full scan with malwarebytes while in safe mode because you have been infected by something that has inserted all those extra entries in your hosts file. SO (copied from a previous answer)
ChuckFickens
Run a full scan with malwarebytes while in safe mode...
You'll be best off using another computer to download the file in the link below and put it on a usb memory stick, or CD. Then start the computer with the problem in safe mode by switching it on and tapping the F8 key straight away. When you get the boot menu select safe mode with networking. Once the computer is started install malwarebytes from the USB stick, or CD and let it update (if you have a earlier version of windows than windows7 wireless won't work for this step, you'll need to connect by Ethernet cable). Once the program has installed and updated run a full scan with it and remove anything it finds.
http://download.cnet....-8022_4-10804572.html