Answer: What you describe might be Pratia, a wonderful groundcover for both sun and shade. It's a creeper and produces tiny blue flowers in the early spring. Of all the groundcovers I have grown, this one is the best!
There is no easy solution for rehabilitating a neglected yard other than to start at one end and work your way through. I'd make it a point to dig in some organic matter after removing the weedy growth. Then plant your favorite plants and water them well. With a little TLC, you can reclaim your yard. Enjoy!
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