Beware of adding too much fill to level out the property. That could cause the two large trees which are presently under water to die. Changing the ground level around tree roots can be fatal to the plant in some cases. This has happened to me.
I think if I were in your situation, I would try putting in some drain pipe runs out to a place where the water can flow to. Could even be the gravel filled trench already mentioned. The grass can grow over it but the drain still works. This was our solution (perforated flexible drain pipe)and has been working great for about 20 years at our home.
Fairly inexpensive repair also. :)
Barney
