The vibration is felt in the seat from 55 - 65 mph, when accelerating. I have new tires, just balanced and rims straightened, so no damage. Is it possible to be the front axles? The passenger side has some play, and the driver's side is much less.

Unless you have AWD (all wheel drive), there is no driveshaft to check. But the inner CV (constant velocity) joints do wear out eventually and will give you a vibration under acceleration. If this problem occurs only when you are accelerating, it is time to replace the axle shaft that is worn. It could be just one or both. If the condition exists under any other circumstance, the suspension and steering components need to be checked as well as the front wheel bearings.

The front tires, will give you a vibration in the steering wheel not the seat..since you re-balanced (assuming it was done the right way) then if your car is a rear wheel drive, it could be a bad universal joint..that is the only other thing that comes to mind...now if you hit the brakes and it vibrates then, then i would be inclined to thinking it would be the brake rotors in the rear....check your u-joints i bet you will find one is either ceased or has play....please keep in mind, when checking u-joints ANY PLAY IS BAD PLAY. any play constitutes replacement...period.

Check out this link guys: http://forums.swedespeed.com/showthread.php?153666-04-S60-R-Vibration&p=1675535
My 06 s60R is doing the exact same thing and $1900 later the dealership couldn't figure it out. I'll be taking it back in and will try to report my findings.