I have a similar problem (I think) and was considering posting a new thread but this is close enough.
I'm in my first year at my new house, and the soil is just horrible. The google street view of the house from a couple years ago shows NOTHING not even weeds growing. I don't know if the real estate people sprayed all the time or what but the soil is just awful. And on top of that the city sprayed herbicide around the edges this year; killed some of my spelt, most of my strawberries, some sunflowers, etc.
I got some weeds in the backyard, and some mulch from when they grew and died. The soil is salty as hell, and I keep digging up chunks of asphalt here and there.
I'm trying to get it looking nice as it's in a public location and use it as a showish garden, but I can barely even get grass to grow.
I put in two raised beds and place plants some stuff in the ground just to see what will grow. I'm thinking I'll try to accumulate yard waste from around town and spread it as a mulch. If I can get wood chips I'll put them wherever there is bare soil.
I'm considering tilling the old soil and mixing
compost with it to fix the structure and then covering with thick mulch.
For the quick results I'm doing the raised beds, and the longer term project is the whole yard. I've heard the best things about composted wood chips, after a couple years just plain chips you can grow in. I'd dump urine around them too to speed things up and get some npk etc with the carbon.