The fact that you're getting a chime (and not a [link|https://www.youtube.com/watch?v=TLjFDPjSN70|"chime of death|new_window=true]") should indicate that the ROM and RAM chips are okay, but you could remove some of the RAM to rule out the possibility of a bad stick that isn't getting caught during the startup check.
Display issues on these machines can usually be attributed to the analog board, how to the capacitors, connections, and other chips look on that?