I think you're going to have to pull the wall plates at every one of your Tv locations and note what color cable is connected to it. In your pics I see black, grey and a thin black on the output side of the splitter. Usually, the orange is used for satellite runs. Why it's hooked to the Tv2 slot has me confused unless it does go to the second Tv's wall plate. The white one you have a hold of should be your input from the roof antenna.
Now, to me, the splitter input should be on the Tv2 connector so it can feed the second Tv (black or grey out) and your outside Tv port (where you would mount one if desired, the left over black or grey) through the splitter.
You may be missing a coax because the "cable" port on the card would now be empty and should be connected to the "cable" in port on the outside (the one you said has the "cable/sat" label). I also see a connector on the wall plate (blue center low resistance connector). What is connected to that? That should be where your satellite cable from the outside should come to. The small black cable coming out of the splitter probably is the antenna wire from your AM/FM/CD/DVD sound system.
The only ports on the card for "inputs" are the "ANT" and "CABLE". Tv1 & Tv2 are outputs to the various Tv locations. The other one (blue center) should be your satellite "IN" (behind the wall plate) & "OUT" (on the front) going to your satellite receiver.
Not to confuse you but, not knowing what color coax comes & goes from what locations makes it difficult. Hence, my suggestion that you pull ALL the plates both inside & out to see what color coax is at each location.