In my parents' bedroom they have Emerson TV, which it CRT, with flat glass 20" screen. I think it's a 2008 or 2009 so it's about 10 years old.

They don't use it much but lately if they turn it on it's fine at first but after about 15-20 minutes it makes a high pitched noise. It even does it on mute. I'm thinking some electronic part must be at the fault.

Sounds like some electrolytic capacitor is dying.