open it and disconect the lights in the front so she wont see its on. you can set up your pc to wake up when qued by the xbox, however the lights will light and the fan will come on. so no good. what is her issue? use a good serge protector and you'll be fine..
She should understand that in your living room all the recepticals in that room are wired together in a daisychain, posibly including the dining room also..so the xbox being on at the same time as the pc is not going to affect much.
my pc stays on all the time, not my lappy but my pc is allways on and avail to share the printer and complete HDD this my lappy and other devices on my secured network.
you could try to tell her that continuously turning the pc on and off is not good for its life span, as it takes more power to boot, start the fans, etc then it does to just constantly run...but not sure if that will help