What you have described are NOT conditions conducive to growing a nice lawn. Lots of sun and good drainage are pretty much basic requirements. Why don't you consider some other, more shade loving groundcover?

With poor drainage and shade forget about a lawn. It will never happen. With the drainage issue most plants are out. If you really want grass consider artificial turf. They have come a long way making this. Now it looks and feels like real grass. I have seen whole lawns of this and unless you are very close up you can't tell the difference

there is a very low growing (flat) Lysimachia minutissima that likes moisture and you can walk on it etc. It also spreads and reseeds. Check out "stepables"

Carla,
I hate difficult growing sites too. Hope you are still around.
How about plants that take foot traffic?
See website as example. Maybe between flat stones like in picture on stepables website.

Try Google search on. Stepables.