Answer: I'm afraid you're facing a real dilema here. It's really important to prepare the soil prior to seeding or sodding and then to keep the seedbed or sod really moist so it will root well. In the case of sod, it helps to roll it with a weighted roller after it is laid so the roots will make good contact with the soil. When this happens, the roots will penetrate even hard clay soils. It doesn't sound as though the soil was prepared properly prior to laying the sod.
The recommended procedure is to rototill the area, spread organic matter (such as compost or aged-manure) over the top and rototil again to incorporate the organic matter. This helps loosen the soil and helps it drain well. If you only rototilled the soil but did not add organic matter, the soil will remain rock-hard once it gets wet and then dries out.
At this point you have two options. Roll the sod up, store it in a shady location and properly prepare the soil. When that's done you can reinstall the sod, roll it to make sure it is touching the top of the soil and then keep it well watered so it can root deeply. Your second option is to rent an aerator. This machine takes plugs out of the soil (and the sod). You can leave the plugs on top of the lawn; they will disintegrate over time and the soil and plant debris will work its way through the lawn to the soil surface. After aerating you can spread sand over the sod and as you water the lawn the sand will work its way down into the holes where the plugs were. The sand will help your soil absorb moisture and will help the area drain well.
Best wishes with your lawn!
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