..........My car starts OK, then after a few mins stops and wont restart for 15 mins. ..........

So, starts cold, heats up, causes something to expand and break the circuit, cools down (15 mins?) and it will remake the circuit so it starts again??? Also, moisture is traditionally the enemy but it CAN make things work briefly until it dries out if it's a track across some vaguely conductive dirt.
Good luck - these intermittent faults can be real sods.