Core aeration might
help. But it sounds like the problem is deeper than a normal aerator can reach.
Toro makes a deep tine aerator, so it must be a common problem. Here's a pic of one. http://www.toro.com/en-us/golf/turf-...-Tine-Aerators
I'd dig a little hole, pour water in it and see how long it takes to drain. If it don't drain there is either a barrier of some sort, or you're near the water table.
I can dig a foot deep hole in my yard, wait 10 minutes and there's 6" of water in it. Pull the cap off of my well and the water is right there!