We have a similar setup in our training room, granted our computer is just on the other side of a wall. But Just buy some USB extension cords or Cat5->USB media converters.

Or something like this, a PS/2 KVM extender
https://www.l-com.com/item.aspx?id=9502

Several different ways of doing this. I'll be more than happy to help guide you if you need it.

-David