1. You do not need a pram battery for the display to work on an SE.

2. You can try the SE's mainboard in your working SE/30.

3. I'm fairly certain that you can use the SE/30 analog board with the SE picture tube and mainboard to see if the analog board is the problem.

4. The analog board is almost certainly the problem. I've found that a lot of them suffer from cold solder joints.