Then check the crank sensor. It gives the signal to the coil. You unplug the coax cable at the ezl and check the resistance between the middle prong and the outside wall.

I say change the cap and rotor because it needs it, and it will solve the no restart when hot problem.

The m103 (your particular m104) needs a tip top ignition system to run right. If the car started when it was parked, and now won't start, either the ignition system got condensation and got corroded, or a mouse ate some wires, particularly the crank sensor.

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Eugene

10 E63 AMG
93 300te 4matic
07 BMW X3
14 Ford F-150 Fx2