Car: 1991 560 SEL, 103500 miles
Problem: hard to start

It does not matter what time of the day is, it always take me three turns to get the car started. On first try, the engine will be on for 1 second and die. On second one, only starter will turn but the engine will not even catch. On the third turn, it will come on but only at 300 to 400 rpm for 10 second. At this time, I would step on gas and everything will be fine from there on. I know the plug wire, rotor, cap are all new. I will pull a plug out tomorrow to check the condition. What else should I check?

It will start right up within 5 minutes of turning engine off. If I park the car for 1 hour, it will again take me three tries to get it started. I know it takes air/spark/fuel/compression to get a car started but I need tips for a step by step diagnostic.

many thanks in advance.