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Hi and welcome to JustAnswer,Thank you for the question and your patience. Should you still need assistance for information purposes only...Initially, is the Sony's screen all blue but with a "...video 3 message..." ?
And, have you also tried unplugging the Fios box?
Have you checked / replaced the connecting cables?
Still, the only easy user doable try of a test would be to temporarily replace the Fios box with another source such as an old VCR, DVD player with similar A/V OUT jacks. The idea is to disconnect the Fios box and using the same cables to the same jacks of the Sony, connect the VCR (or DVD player or camera or game console).
If the "...black with a video message..." symptom persist, then it would be an internal hardware issue with the KV-36FS100.
Please post back results / observations of the above once tried.