So I bought a north facing, poorly maintained house in October 2020, meaning the neglected backyard faces south with little to no shade. The only shade that the yard does get is from the woody weeds that have grown into the back fence between my backyard neighbor and I (I've actually found that some of these weeds are mulberry trees, while the other was just a weed the size of a small tree). I assume the soil is bleached of all nutrients due to constant sun exposure and it being extremely sandy. The lawn is compact and so lumpy that it holds a lot water when the snow melts in the lower parts of yard, which drains/thaws into my garage causing ice to form around the garage, on the garage floor and on the driveway. The lawn is mostly dirt patches, weeds, and some turf. I believe the higher parts of the lawn had been caused by organic material building up from the mulberry trees and the woody weeds dropping their leaves because I can see on the other side of the chain link fence that my neighbors lawn is an inch or two lower than mine. I'm at a loss on what to do. I can't just add topsoil or sand to the low parts of the yard because then as the snow melts, it will melt into my garage more then what is already is. I'm thinking of rototilling it, grading it and adding nutrients back into the soil to ensure a fresh new start. I have a small budget due to the home needing major repairs as well so any suggestions would be appreciated! Thanks!