With a little hackery, this is often possible. What you do is generate CVBS using a little combiner circuit, apply that to the composite input to get the thing to generate all the deflection, then yank the existing RGB lines and apply RGB video to them directly. As boardjunkie said, a video amp will likely be required. You will also need to run the set off an isolation transformer, otherwise you'll very likely end up with a ground loop that will damage/destroy your video card and possibly you, too. I can't find any docs on the LA7673 IC you have pictured (nor can I read any of the others), it's difficult to know much about how this set works. It might not be the best candidate for this kind of modification.
EDIT: Oh wait, this thing doesn't even have a composite video input. I wouldn't bother with this thing at all.