2004 Chrysler Crossfire Check Engine Light

I have a problem with my 2004 Crossfire. It has an intermittent 'Check Engine' light that comes on about half the time when I start it up. Sometimes it will also come on in the middle of a drive. And then sometimes it will NOT come on for about a week, or even more. I have tried tightening the gas cap (in the manual it says try this first) and it's not a problem originating there. Every time I get ready to take it into the Dealership on my day off, the light does NOT come on! And the last time I left it with them and paid for a rental car for 2 days, they said they could find NOTHING wrong and NO LIGHT COMING ON. I am getting scared that this might be a major problem in the making, and that I need to do more. I had to recently replace the entire key mechanism on the driveshaft, as it broke and was very expensive. The warranty on this car was for 3 years or 36,000 miles, whichever came first - and of course, I am out of warranty because I've had the car for more than 3 years - even though it's still under 36,000 miles. I bought an extended (non-factory) warranty from a private company but I'm afraid they are going to give me major hassles about getting this fixed in a timely manner. Is there ANY WAY for me to diagnose this problem myself so I know what I am dealing with before taking it in to these bozos again? PLEASE ADVISE, I REALLY APPRECIATE IT, THANKS.