With out being able to lay hands on it, my first inclinations are either PCM or SKIM. If the SKIM module went bad it could make it die and then after 3 starts it will lock out the PCM from starting or even cranking.
If the PCM dies it could cause this issue. You're going to need a scan tool to see if you can communicate with PCM or SKIM. Could also have a blown fuse for the PCM. That will cause the same issue.
