99 Regal LS 3.8

HELP!!
Ongoing, intermittent problem...morning commute goes great, come out of work and car wont start. I have full electrical, all normal dash lights, engine tries to turn over then....nothing. Crazy thing is, on 3 occasions once the vehicle is tipped to go onto the tow truck, it will start fine.

I've tried using my other set of PAS chipped keys.Doesnt seem to matter which set I use. Mechanics never find any codes whether we've managed to restart it or not.
Any Ideas??:1zhelp:

I would have the battery and battery connections checked. You may have a plate inside it that has broken loose and shorting out. Then when you tip the car, the plate moves back into normal positon, and the car starts.