Answer to: What type of power cord does this use?Ebay sells everything. Craigslist too. Put the model number in the search bar and search for it. If you can't find it there, go back to where you bought the computer from and order another one off of their site. Edit: try here http://www.laptoprescue.com/laptop-adapters.php
Answer to: usb connector is brokenIf you hadn't ripped the contacts, you might have been able to solder it back on, but this is pretty bad damage so unless you replaced the entire board, there's no chance.
Answer to: Why does my Xbox not turn off?If it's not turning off via the power button, you may not be pressing it hard enough, there may be something stuck inside of the button or maybe the button is just plain broken. Either way, the XBOX is not like a computer, you can shut it down using the button, so turning it off by unplugging the power is like the same as unplugging it and shouldn't be damaging unless you do so while it's saving data.