Reny, the battery seems to be OK as it normally started after you let it sit awhile, as does the voltage regulator since the battery is recharging. Out of curiosity when was the last time you replaced both?
See if the gear shift selector position has any effect on the engine starting ... wiggle it, or with your foot on the brake and the key in position to light all the dash warning lights move the shifter to "N" and see if the engine will start. Our 124's start in the neutral position so it may be related to a gearshift position switch although from your description it would seem to be engine temperature-related.
When you say "I hear the sound to start but the engine does nothing." does that mean you hear the fuel pump running?
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Fred Hoelzle
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