I would look at the neutral safety switch since you have an automatic.  The
rolling technique that worked for awhile probably jarred the switch that
prevents starting in gear.  It may just be out of adjustment from wear.
This switch could be by-passed for diagnostic purposes.  Next time it is
dead, jiggle the shift lever.  Move it out of Park and back a few times.
Another common problem is the ignition switch.  They can cause all kinds of
intermittant electrical problems.
                                                   Good Luck