Looks like some serious drainage issues. I'm far from a landscaper, but I would clear everything out all the way to dirt. Spray a herbicide, wait a month, or build a wall edging in the mean time. Haul in several tons of soil and level off the whole lawn, use the wall as a barricade. Lay sod over the top of the level soil. Possibly install irrigation before. (Something I didn't do, and I can tell you from experience it's a mess keeping sod moist for a month straight by regular sprinklers, but can be done.) Hopefully I can give some useful advice from the valuable information people have gave to me around here and take a little time off of their hands because I know Agrostics and a few of you others are BUSY outside.