It sounds to me like it is definitely failing at the board somewhere. When you replaced burnt connectors, did you reflow solder on the back side as well? Could be other things wrong with the board, and let's be honest, they are old and brittle at this point.

You may consider investing in a replacement MPU/Controller board (Rottendog, etc.). I know it costs 200-300 or so, but boy that has resolved a lot of headaches for me with machines of that era. It will cost you close to that to have someone else repair it, and it will still be old.