The Icemaker in my Frigidaire refrigerator has never worked since I bought the house, the problem is that the coils keep freezing over (the icemaker is in the refrigerator compartment so has its own freezer coil to make it cold)

I spent a weekend pulling it out, thawing everything out, and then replacing the defroster coil, thinking that would fix it. It didn't -- it worked for about a week afterwards until freezing over again.