No, it's likely not broken. Your generator has a power-saving feature for the display.
After a few minutes of inactivity, the LCD screen switches to a power-saving mode and shuts off to conserve energy. This does not affect the generator's performance—it's still running. To wake the screen back up, just touch it at any point. The LCD will turn on.
If that didn't work: If touching the screen does not bring it back, then check your power source and remote control connections as outlined in the first answer. A complete system shutdown would also blank the screen.
Heads up: The screen is part of the control panel, which can be reversed 180 degrees for wall mount installations. If you recently moved the unit, be careful not to disconnect the LCD wires when reversing the panel.