Landscaping - How to Correct Heavily Flooded Yard
If your jurisdiction's drainage code permits it, you could install a yard drain in your yard.  You would need to slope the lawn so that in a light rain (such that the water can eventually be absorbed by the topsoil) the water does not drain into the drain, but that if enough water collects on the lawn to be a problem, the excess does drain into the drain.  You would also need to pipe the drain water to where your roof drain goes to.  (This is why you should check with your jurisdiction about its drainage requirements.)

Also, is your topsoil well aerated?  Compacted and/or clayey topsoil often does not absorb water well.  You might want to consider aerating your lawn, or even replacing the top 8" - 12" of your topsoil with a sandier, more organic mix that is designed for drainage.