Usually, and AMTT display doesn't just "go out". Normally, it begins where you will get vertical stripes that are blank, and eventually it goes bad. If the display is completely dark and depending on where you live, I suspect temperatures may be involved. On the display, there is a temp sensor that could to bad. It plugs into the back as wires 705, 706 and 707 and that plugs into J11 on the I/O board. You may want to reseat that connection. There is an additional outdoor air temp sensor plugged into J13. You could try temporarily plugging that into J11 to see if it changes anything.
If that doesn't fix it, next I'd look at the CPU board. You should find 4 socketed connectors identified as U3, U4, U5 and U6. Each of those handle different processes through the I/O board. It's possible one of those may not be fully seated. Support the chip on the back side of the board, and gently push them in to ensure they are fully seated. They should click. Next, you will see the program and bitmap chip sockets in the center of the board. Look at the corners of those sockets. If they get cracked, you should be able to detect a small line in one of the corners, and it's often when it gets colder where it could cause issues if they are. The chips can move just a bit and it's possible to have strange symptoms such as the display not coming on (or any number of other issues). If the socket is cracked, the only way to repair it would be by replacing the board.
Unfortunately, we no longer have parts available for an AMTT, but you may be able to find them or get yours reworked through someone like RDM.