a pretty regular problem and one that will cause down the road problems if not addressed now. You do need to raise the ground level to reduce and eliminate the ponding of water. A good solution would be a float controlled pump that automatically pumps out the water when needed, BUT you pretty well nixed this idea. You need a place down hill to send it.
Now, I would not even think about the blown in cement. Too expensive and cause problems.
I would consider finding some day labors in your area and hauling in many many yards of sand or sandy loam in and manually taking the stuff in and leveling and packing it in. This will be quite an undertaking that is for sure, but with a bucket brigade and cheap labor, it could happen. The quality control part on your side will be to make sure the stuff is packed down and even lightly watered in to cause settling so you are doing a good job in raising the ground level. Then too, having a good working gutter system and extensions to take the down spouts away from the house is another thing to do to make this a total system program.