Toshiba, rear projection 50", 13 yrs old, no video on HDMI. Graphics appear while Chromecast or Firestick are booting. No vid

[Rmns8_36]

Old TV, HDMI port no vid

 

[americanaudiophile]

If you are getting video from other sources the streaming sticks may be set to output in higher video resolution than the TV can accept. You could try to plug them into a new set and change the resolution to the the native resolution of your TV.
If there is no video period I think it's time to get a new TV. It would certainly be cheaper than repair and boards for are not likely to be available. Lots of used sets on Craigslist.