the "computer controlled start" is like that.... basically a "hit" of the start, causes the computer to start an initiated crank which lasts for about 2-3 seconds (I think). After which, if it hasn't started (computer detects this), the computer shuts the starter back down. This should be your normal "start procedure" (ie. hit the start).
Anyway, as suggested, it appears you have issues in and around the key / wiring thereof. Having said that... it is likely NOT ground related. It is more likely voltage / power related as that is what is being sent to the pcm to detect the "hit". Having said that, ultimately, the pcm does send a ground to start relay to get the process going.
Rereading your latest reply... "it cranks but never starts".... this symptom is different that the title which started the thread. So are you saying now that you no longer see a "delayed" start and now have a "crank but no start" issue? If so, you can disregard what I mentioned earlier, you need to follow a "crank but no start" troubleshoot.