Something like that is happening to my 98 lumina. One morning I unlock the car with the remote and when I tried to start it it did not work. It seemed like it was dead. After trying several times I got it working. Once I turned it off I locked it and then unlocked it with the remote and once again I was not able to start the engine. Then, by accident I figure out that if I did not lock it using the remote, it would start like always. However, I am uncertain on what the problem is ...