I have a 2004 Lexus IS300 around 75,000 miles that's had regular and up to date maintenance. Around three months ago the one and only key I have broke off of the case. We taped the case completely and were holding the key with the case to start the ignition just until I was able to get around to buying a new key and having it cut etc. Well, today I drove to a few different places around town with no problems at all until after I pumped gas. The car started afterwards with no issues and I drove about 1/4 of a mile and came to a stop. As I went to accelerate, the car started violently shaking. Seemingly originating from the back and would not accelerate. I restarted the car twice and both times it turned over and then immediately shut off. I had the car towed to our local Toyota dealership where they did a thorough inspection, especially of the timing belt which is what they originally suspected and they detected no problems mechanically. They have told me the whole problem is my key and that there is a problem with the transponder in the fob (although I've not had any issues with the broken key for around three months). I understand I need a new key but could the transponder problem ( I'm assuming they think it is now bad.) Be the reason my car suddenly started shaking and smoking a little (white) from the tailpipe? Thank you so much! Sorry so long!