Why are most of my cable/coax wires disconnected?
Because you only hook up what you have to, to avoid signal loss. If you're serious about getting HD to all your jacks, you should probably look into getting a powered splitter.

Otherwise, you just want a small passive splitter in a good MHz range. Over 2k was bare minimum last time I checked. 

I have internet cable and I want it as clean as possible, so I use a good two-way splitter to feed the modem and then it feeds another one I had laying around for the giant jumble of TV feeds.

You probably have one or two incomings at most. Unless someone wired your house up for something strange, this is no different than many people's basements I've seen. Where there is either no equipment yet, or it's just like 4 out of the 16 cables run into a passive splitter (cause those things are cheap and cable guys charge ~$5 a termination on the cable ends, so frankly I'm surprised yours all are. Welcome to your new house? ;).



If you move out, you might take your expensive 12-way splitter with you. If it's a new construction house, that's why there's nothing there yet.