Bought a house (built in 1937) recently.

When the clothes washer runs (particularly, when it agitates), lights in the house flicker.

I've read in numerous places online that this is possibly due to a loose neutral somewhere.

Would that kind of power flicker kill my fridge? The freezer keeps cold, but not the fridge, and I'm almost certain it's due to the control board dying. My impression is that poor power stability can kill control boards in appliances (I'm pretty sure it happened in our previous house, to a fridge).

I'm asking because I want to know if I need to get the flickering fixed before I get the fridge fixed.