I have a 2004 LeSabre w/ 35,000 miles. The car had a shimmy/shake that the dealer said was from worn tires. I replaced the tires w/Michelin Hydroedge tires, which were road-force balanced and filled w/ nitrogen. I just took the car on it's first new-tires trip (400 miles)and found the problem still exists. Steering wheel and driver's seat shimmy/shake that sets in at about 65 MPH. The car is a hand-me-down and has never been in an accident that I know of. The only contributing factor to the problem may be weak front shocks, but I'm told soft front shocks are the norm for these cars and mine are OK.
Does anyone have any idea(s) of what the problem(s) might be?