Was there any resolution on this? My wife's 2010 G6 GT is having this exact problem. Every other day or so, the car will crank but not start. The temporary fix is removing and reseating the fuel pump relay in the trunk fuse box. It will go several start cycles but will fail again within a few days. Taking out and reseating the relay enables it to start again. I don't believe it is the fuel pump because it runs fine once started. I have replaced the relay but that did not fix it. Could it be related to the anti-theft system, like it somehow forgets her key? If so, why would reseating the fuel pump relay fix this? Confused in Indiana. Thanks for any suggestions.