I know very little about pinball repair.
That won't last long.
I trust you have been here? Read it, poke around your machine, go back and read it again and start all over. Buy a DMM if you don't have one cuz you are going to need it.
http://www.pinrepair.com/de/index.htm
On the display problem, lots of things to check before you start worrying about diodes. Proper voltages ? cables oriented correctly and working? Is it possible the displays themselves are trashed? Unfortunately, you are going to have to follow the guide to narrow down the problem beyond "it doesn't work".
I'm not familiar with the "cooling towers" mech on this machine, but the first thing I'd check would be the switches. I'm guessing when the ball enters this toy, there is some switch that has to be "made" to signify that. Check the operation and wiring of that switch first using the switch test. If the switch looks good, check for mechanical binding or gummed up mechanisms.
In *my* experience, 99% of all problems I need to fix have nothing to do with diodes or transistors or any kind of board work. It's usually something simple. Eliminate those things first and things get a lot easier.
If you are motivated to learn, you can do it. Good luck and enjoy!