1996 Oldsmobile Achieva Starting

Electrical problem
1996 Oldsmobile Achieva 6 cyl Automatic 130000 miles

When have to hit the ignition 3-5 times. Let it sit for 10-15 minutes and then it starts. We have replaced the starter, relays and ignition. It seems to have something to do with the key. If we do not turn the key completely off, it will restart easily. If we shut it completely off it takes several attempts, letting it sit and then it starts.