1988 300CE won't start

Hi there...I recently purchased a 1988 Mercedes 300 CE with 126,000 miles on it.....the car runs beautifully ..idles well...no miss fires...went out the other morning...it started fine...stopped the car to run an errand...came back...the car would try to turn over but not fire...almost like it was out of petrol..I thought perhaps the petrol gage was reading wrong..I added some petrol and it started fine...ran like it always does...changed the fluids and filters...car ran fine until it was time to back it out of the garage...it did the same thing....like it was out of gas...I understand the fuel relay is a pesky sort...what else should I look at in the this situation??? any other parts that could be causing the car to act like this??? Do I need to recalibrate the brain??? Thankyou in advance

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