I have a GE Porfile Artica and I do not have lights on the refrigerator side but, I do have lights in the freezer side. Also the digital display does not show anything. I had replaced the circuit board about 2 years ago because the refrigerator was not cooling. I tried to replace the bulb but nothing.
It might be the light switch or it could be the center contact on the light socket isn’t tall enough to make contact with the bulb.
The new light bulbs have very little solder on their bottoms these days. This video shows how to bend the tab up a little to make better contact.
Always unplug the refrig. before working on it.