Even though this is a bad idea, certainly there is a way.
You controlled computer should act as a network server, and your controlling computer — as a client, the server performing keyboard and mouse input on its local computer by request from a client.
Therefore, you can develop and install on a server host some Windows Service working as a network service.
For simulation of keyboard and mouse input, use P/Invoked Windows API
For networking, you can use sockets, classical remoting or WPF, self-hosted by your Windows Service. Please see my overview of these approaches in my past solutions:
how i can send byte to other pc
Communication b/w two Windows applications on LAN.
For development of Windows Service, start here: http://msdn.microsoft.com/en-us/library/y817hyb6%28v=VS.100%29.aspx