Yep it's the solenoid. Happened to my grandma's 02 GT with only 35K on the clock. They had a hard time figuring out what it was because after the car was shut off the problem went away and wouldn't come back for a few weeks or months. Finally they brought it right in after it happened and it was the solenoid. $700 to get it replaced at the dealer and that's with the discount they give my grandpa. Don't know how much a new solenoid is or how much work it is to put a new one in but I guarantee you'll be happier doing it yourself instead of paying $700.