Wiring – Where should shielded data cables be grounded

The sub panel will need the ground to be separated from the neutral. The only place they are joined is inside the main breaker panel. This prevents open neutrals between the main and sub panel from sending current over the ground, and possibly electrocuting someone if a better path to ground can be found.

For the 3 way switch, I'm guessing you need to trace more wires, or you have a smart switch of some kind. You'll need to check the switches first, and then start tracing the cables on each end to see where they go. I'm guessing a second line is running just for the 3 way switch that you haven't found.

This is a bigger can of worms than meets the eye. There are huge arguments over all this.

This is a coax grounding block:

This is a grounding bar:

This is a grounding bridge, your cable company or telephone company probably has one on the outside of the house at the electrical service entrance:

What I'd do:

• Run a ground cable from your frame to the grounding bridge. Use the biggest cable that will fit properly in the bridge. Don't use A-D above.
• Install a grounding bar that will handle that wire, at your frame in the basement.
• Run a ground wire from your metal patch panel rack to the grounding bar, use grounding lugs on the rack. Probably not necessary, but use Noalox between the lug and the rack. Remove paint if you want to go all in.
• Install and ground coax grounding blocks for your antenna and CATV service.
• Use good quality surge strips, at the frame and through the house, and check your outlets with a receptacle tester to make sure they have ground wires - surge strips generally don't work without a good ground.
• If any of your equipment has a grounding lug on the back, ground it. (For example, many of the Netgear metal cased switches have a ground lug on them.) AFAIK only necessary on equipment with a two wire power plug.
• Remember, holy wars over all this - some will say this is all totally wrong. This is what I would do though after following all the arguments.

Edit:

There is a good chance your patch panel doesn't ground the coax that goes through the house. However if you use surge strips that have a coax port in those places, and the coax has been terminated properly so the body of the plugs are bonded well to the shiled, and the outlets those surge strips plug into have a good ground, you should be fine.

One last thing - this whole thing hinges on good grounding of your electrical system. If you want to be really careful there, have an electrician check the grounding and bonding and if possible ground resistance. This is IMO worth doing in general.