How should I go about troubleshooting? Thanks in advance for your advice.
Well, that's a wild ride for sure. I think the best thing to do here is start at the beginning. I think the board is working if you have the breakpoint hitting. So at least we have a good idea that the launchpad board itself and the onboard programmer work. I would remove anything connected to it and run via USB for a bit while sorting things out. You will need to set the power jumpers to the default positions to power the board from USB.
From there, use one of the launchpad board examples that come with the IDE and make sure you can do a build/flash/run with known good setup. Something super simple like blink an LED is plenty. Flash it to the Launchpad, not just run from memory. We want to check that part of the board/chip as well.
If that works, triple check all the jumpers and switches. I don't think they are necessary for the display board to work, but it's a good place to start. Set them as directed by Clough42. From here, you can connect the PCB from him for power and interfacing. Tripple check that it's lined up properly. It CAN be installed one pin off, for example. Disconnect everything else though. Now check with the existing program for the LED blink or whatever. We want to be sure the Launchpad is getting power and working still.
Now add the display board. How are you wiring it? I found that how it's connected matters a great deal and it's pretty easy to get interference and mess up the display etc.. It doesn't damage anything, but it also doesn't work right. Start with short jumper wires direct to the interface board. No more than 6" or so. If that works, we can start looking at wiring.
With electronics/programming, troubleshooting is usually start from the simplest setup and build up one part at a time until it breaks. Now you know what is wrong and can look at fixing it. Lets get the display working and we can start on the mechanical bits.