Why do the scores on my Atari 2600 games have random symbols in them that don't resemble numbers?
If you can find an Atari Hangman or Surround cartridge, you may want to see what happens when you play those. I would not expect that the memory within a 2600's RIOT (RAM+I/O+Timer) chip would be likely to go bad, but if those games exhibit "stuck" pixels, bad memory would be the only likely explanation. I suggest those games in particular because they use a significant portion of the system's RAM to display a bitmap, and any problems in those portions of the RAM would manifest themselves as stuck pixels without any other side-effects.