I doubt you can make the TV card input socket output anything without low-level access to the card’s firmware and possibly some hardware hacking. Certainly not with Java, and even if you could, there are easier ways to output a video signal from a computer.
Nonetheless, assuming your TV has a tuner (i.e. it’s not just a monitor), you can always plug the aerial into the TV as well. All you need is a BNC T-piece (e.g.) and an extra length of cable. That way, your aerial goes to both the TV and the computer. As a bonus, you’ll be able to get a different channels on both.
[edit]Having re-read your question, I think I’m barking up the wrong tree. Is what you want to do use your TV card to use your TV as essentially an external monitor? I doubt very much that this is possible. The card isn’t designed to transmit a signal – it’s designed to receive only (unlike, say, a network adapter, which is two-way). Nice as it would be, having the connectors is only part of the story (an analogy would be trying to use a scanner as a printer – both involve images, but one is for inputting images, while the other is for outputting images). You’ll be far easier buying some sort of video over IP system, as has already been suggested by others.