This solution may only works if you already confirmed or tried replacing the LCD screen module and then you can still hear a tones or audio from the device.
The Nokia 6303 classic circuit layout, there is no EMI/ESD filter chips is being used, the display data signals are feeds directly from the CPU (RAPStack IC).
Nokia 6303 classic Display Connection Tracks
Some hints on how to fix the Nokia 6303 classic with display problem:
1. Check/replace and ensure the the LCD is working.
2. Calibrate the phones firmware, flash, restore and update it.
3. Visually check, clean or re-solder the LCD pin connector.
4. Check and trace the LCD supply voltages (VAUX 2.78V and VIO 1.8V) from the LCD pin connector down to the capacitor near the Power IC (AVILMA).
5. If all above procedure didn't solved, the possible faulty is the CPU IC (RAPStack). A re-hot, rework or replacing it, might only fix the problem.