My sister's '94 Olds Ciera had a problem just like the one you describe.
Caught it in the act one day last week.  Motor showed open on my VOM.
Plugged it back in and gave the motor a whack with my fist.  It started and
ran.  That told me the motor commutator or the brushes were in bad shape or
else there was an open winding in the armature.  Evidently the motor
occasionally was coming to rest on the "bad" spot and refused to start until
normal vehicle vibrations randomly caused the rotor to shift position ever
so slightly.  Replaced the motor with a new one from Advance.  All is well
again.