Did you re-flash the stock firmware? If so, then it's most likely not the programming or firmware.
The RAMBo is a circuit board, and components on circuit boards can go bad. If that happened to components that directly affect the LCD pins, then you'd have trouble.
You could try replacing the RAMBo board to logically determine if that's the problem. If you do and you still have the same problem, you know the problem is elsewhere. But given the other troubleshooting steps you've tried, that is possible.
And I guess that a delta machine is always noisier than a Cartesian printer because it runs all 3 motors all the time. I think the firmware has some kind of an impact. I remember that the Prusa MK2 has different run modes in the firmware settings that impact the noise level. Running the motors in the low power mode makes the printer very quiet. I wonder, if that can be done on a Rostock, possibly by using Marlin instead of Repetier.