If the rom contents would have been lost, it wouldn't show any activity at all. (Besides perhaps random pixels lighting up.) Have you checked that small chip in the socket? It could be a I2C eeprom or an fram that stores the messages. Could you just check the number written on that chip? As the thing has a serial interface, there was a way to load custom messages. I doubt they hardcoded the messages in the microcontroller firmware. Nowadays, it's common that those controllers have buildin eeproms, but when the display was designed, they might have used a separate chip. The scrolling letters and numbers could be a sort of display test with an unprogrammed message, or could be the eeprom that stored it's memory adresses into it's memory cells. Besides the numbers and letters, do you see any other ascii characters on the display?
If the display is using a separate eeprom or fram chip, it might be possible to analyse the contents of one and recreate some usefull text by program another one using an external eeprom programmer. The text will probably be plain ascii, but they might use some special control codes to choose the color of the display, make a text blink on it or make it scroll in vertically instead of horizontally. It depends upon the options the display was having. If you are unlucky, there could be a checksum or crc on the contents of the chip.