1992 Other Oldsmobile Models car occassionally will not star

1992 Other Oldsmobile Models V8 All Wheel Drive Automatic

I have a 1992 Oldsmobile "98", with the computer chip ignition key. Lately when I drive the car and stop and turn it off, it will not start back up. Sometimes I can drive and stop and start several times and it works just fine. It naturally will not restart at the most inconvenient time. I am getting leery of driving it anymore for fear it will not restart. When this problem happens, all the dashboard lights work, but there is no sound and the car will not start. My mechanic says he has to check it WHEN that happens to see if it is the starter. Like I mentioned before, it never happens when he is available to check it. I suspect it is either the computer chip key or something in the ignition switch. Anyone else ever have this problem? Thanks.