KS07078 wrote:... My TV is connected to the HD set top box ... The STB has multiple ports in the back including a ethernet port ...
... There are some contents that are available only on the internet ...is there a way to watch the internet stream on the TV (through the STB) instead of having to get it on the computer and connecting the computer to the TV as a display? ...
Unfortunately, no. At this time the only valid input to any STB or DVR is coax from the ONT (Verizon "main" box), often via a splitter as in your network. It's possible that new STB software may offer this in the future, but not just yet. Verizon has discussed something called Verizon Media Server that may have streaming capability, but that system is not yet released.
There are as you've noted other rear outputs on STBs that can send signals to display or recording devices (over coax, composite, component, or HDMI cables). But all other inputs to the STB other than coax are disabled.
This leaves you with the following choices for streamed content. You can use your computer as you mentioned. You can also try Roku or AppleTV; both can supply various streaming services. You can try a Blu-Ray player that offers streaming services similar to Roku and AppleTV. Finally, if your TV is "smart" enabled, you can connect directly via Ethernet or wireless to the network and the Internet.