So I take it that you're going to mirror the display from the eMac on to another display, and you also want that display to be used for your PC? If so then as long as you don't want to use the eMac for for the PC then you can buy whats called a KVM(Keyboard, Video, Mouse) Switch. This will allow you to use the display on both computers. It doesn't reply on one computer or the other being turned on. What ever port is receiving a signal will kick the display on and start displaying a picture.
You can also use the same mouse and keyboard depending on if you get a KVM Switch with USB on it instead of PS/2. There are all kinds of different KVM switches. Some have VGA w/USB, others with VGA w/PS2, some with DVI w/PS2, others with DVI w/USB, there's even some with audio line in/out ports on them so you can use the same set of speakers with 2 different computers. It just depends on how much money you want spend. They range in prices from $40 to $500+.