If you are looking for a standalone Linux box just to turn on a lamp I think you are over-thinking things. Check out X10 automation kits: here's one for ~$24.
You should be able to control that with a small script (python, perl, etc. anything that can write to a serial port) that you keep running on any computer in your parents' or your own home. X10's advertising is notoriously lowbrow, but the hardware itself is decent and a little googling will find you a lot of hackers that have done crazy stuff with it.
I cannot persuade my parents to keep their computer on 24/7. That is the issue that I am trying to sidestep.
However thanks for the X10 link, it looks very interesting.
http://www.google.com/products/catalog?hl=en&q=x10+pc+in...
You should be able to control that with a small script (python, perl, etc. anything that can write to a serial port) that you keep running on any computer in your parents' or your own home. X10's advertising is notoriously lowbrow, but the hardware itself is decent and a little googling will find you a lot of hackers that have done crazy stuff with it.