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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, bear with us; re-confirm and post back with the complete model number of the RCA TV.
Is the "...blank screen..." blue, black or white?
Consider an experiment (if have not been done). Power on the TV and set to a program/channel. If at all possible, darken the room where the TV is. Wait for about 5 minutes or more and until "...blank screen...". Shine a flashlight at an angle (not directly) and nearly but not touching the screen where the volume level / menu display is usually seen.
Press the VOL UP/DOWN or MENU button and note if a dark/ghostly image of the volume level or MENU could be seen.
Please postback results.
The above is a test to determine if it is a backlighting issue.