keep in mind that the issue could be with your TV, and not necessarily with FIOS. I have read where some people have not been able to get a picture via HDMI when connecting the FIOS box to their TV (although those TVs were all Samsungs).
But just as the other posters mentioned, you should be connecting the DVD player directly to the tv.
Your TV should have several inputs. If you can provide the model # for your RCA, then I take look at the specs online and tell where each should be plugged into.
But first, I would try connecting the DVD player directly to your TV via HDMI. HDMI carries both audio and video signals. Component wires (red, blue, green) only carry video.
Hope this helps.