Vibration/noise, high speed

I recently purchased an '03 LincolnLS, v6 with a mere 37000 miles on it and NO damage.

It has a high speed vibration throughout the car starting at 72 mph. Tires were balanced, then rotated with no relief. A new set of tires did not correct the problem. Any ideas?

This car is RWD, correct? A slight unbalance in the drive shaft, or a bad U-joint, could cause this.

I agree with mcparadise.
The driveshaft was balanced at the factory, but over the past 6 years or so, it is certainly possible for one or more of the balance weights on the shaft to have come loose. And, as mcp stated, a bad u-joint could also cause this problem.

I guess I was thinking with only 37000 miles the drive shaft would be a long shot but it does feel like a shaft problem