It reminded me a tiny bit of Interstate 60, but that was Gary Oldman's bike ran over by a truck after Michael J Fox open's the car door, the more I think about it, it is nothing like it, but it is a great film!
Rereading what you wrote, it really does sound exactly like Pay it Forward .. type opening scene in google and exactly what comes up is what you describe.
Then I was thinking Mr. Destiny with James Belushi, but his car only stalls then it goes in another direction, there is no car given....