I'm having exactly the same problem with my mpv 2001. I already had the starter replaced and it continues to happen sporadically. My mechanic said it could be a number of problems such as the ignition switch, solenoid, computer issues. He cannot fix it unless he heards it. He had it in the shop all day and he couldn't replicate the problem. Of course it only happens when its out of the shop.
He doesn't advise changing everything because it is hit and miss.
Did you find a solution to your problem yet.
Would appreciate your help.