Jim, I'm an independent contractor for DirecTV and Hughesnet installations and service work. While I don't know which cable company you are with or what technology they use in your area there are a few things to check.
Look into each connector and be sure that there isn't any stray strands of the wire shielding (or in some cases the foil shielding) that are touching the center connector. If there are any use the tip of a knife to trim them or remove them.
Run your fingers down the outside of the parts of the cables you can reach. You may find a spot where the cable was crushed or bent too tight. Because the center conductor is encased in a dense foam core it can be stretched and broken by a tight bend in the cable since it can't move freely to relieve the stress. You'll feel most of these defects better than you'll see them.
Disconnect all the connections and reconnect them. For reasons no one understands that can help even if nothing else gets changed.
Shut off, unplug and restart all the electronic components- the boxes, modem, TV etc.
Is your computer plugged into the same outlet or power strip as the TV? Sometimes the electrical harmonics from the computer fan or the computer monitor can cause the TV fits. It's rare but worth checking.
Consider disconnecting all the hardware that is related to the computer and modem and see if the TV works. At least that will let you know if the problem is in the service and its wiring or if it is related to the computer hardware.
When you call the cable company be prepared to explain what equipment you have, how it is connected and what you changed. Unfortunately the folks who answer the phone are generally reading from a script on a computer screen and they are not technicians. Ask for a tech.
Also, the folks who answer the phone often cannot make a decision. Ask for a supervisor if you don't like the answers you get. If that fails, ask for the customer retention department. All outfits have one although the name may be different. Everyone in the industry knows it costs a lot more to get a new customer than to keep you happy so those are the folks who can really make things happen.
Good Luck
Lance
Once you've