Alright, well I figured it out. I must say though, this forum was absolutely no help. Over 40 people have looked at my question, but no answers. I belong to a bunch of other groups regarding other subjects, and yes the newbs can be annoying at times, but the whole purpose of these forums is to answer questions.
Before you scream to yourself....I did look around. Consequently, I found nothing about tv tuner cards, and everything about video capture dealt with DVR cards. I don't need a DVR (not recording, only have 1 camera), so was asking about the ATI TV Wonder I have.
Anyhow, enough ***ing. I will post the solution so if anyone else has this issue, it will be solved.
The problem with connecting a BNC to F-type coax is actually not a problem. A physical connection is enough. The problem is that when using a tv tuner card (or when hooking it up to a TV) the circuit expects a modulated signal (ie. more than 1 channel in it) so it tries to split up by frequencies. The signal from the camera is just one signal. So, going from BNC to coax (to a coax input) is not adequate, but if you throw another converter (of just convert immediately) to an RCA (composite) and plug it in to the appropriate jack (in a TV, VCR, receiver, capture card, whatever) it WILL work and what you do with the signal from there is up to you.
Hope this helps someone else.