Brand of computer that will auto power on and shutdown
There is no brand of computer that has been manufactured to auto power on and shut down. A computer device mostly depends on instructions given to it to perform a particular task. in this case you can only use applications that can let you control your computer to auto start and shutdown.
One of these automation software is from lifesoft which has both features that you need, you only need to buy a copy and install it onto your system.