Here is how it is supposed to work:
The digital display comes on at full brightness when the car is on and the headlamps are off, but the buttons don't come on until the headlamps are turned on, at which point the digital display dims and becomes variable.
If the digital display does not come on when you turn the car on when the headlamps are off, your problem is a bit more complicated.
If your symptoms exist only when the headlamps are on, it is likely a poor interior lamps connection at the rear of the stereo, and I would test it with an electrical test lamp when you are having the problem.
1999 540iA Sport
Former 93 SSEi Owner
Former 89 SE Owner