Jonathan,
A bit of what's confusing me and Grant is what exactly is connected where? We wonder if you have the terminology correct.
iMac G3s are really old machines that look like, and may come in a variety of case colors, but still have this generic shape:
Mac Pros are desktop machines that look like:
From your initial post, it sounds like you are getting the TV feed normally on an iMac G3, as shown above, and are trying to get it on a Mac Pro desktop.
TV feeds often come in Quicktime, Realplayer, or Windows media player playback, and sometimes Adobe Flash. Do you have any idea what video format the TV feed is sent at?
For instance, Mac Pros do not support the older Quicktime Indeo Video format because it required a plugin only made for Classic, which the iMac G3 supported. And Indeo went out of business. Newer formats you would not have such a problem. Could this be part of your problem? I didn't see the Mac Pro on your initial post, so I wasn't exactly sure what was being hooked up where.
Are the computers themselves all working? Or are you trying to hook an iMac G3 to a Mac Pro and get video off of it? Or do I have what you are trying to do all wrong?