Do I have a bad fuel distributor..?

[mauka]

1991 300SL about 117,000 miles. Basically a cold start problem. In the morning, or after it has sat awhile, I've found that if I turn the key on and wait a moment untill all the noise stops, (I don't crank the engin) and then turn the key to off position and back on one more time...the car then will start upon cranking the ignition. However, sometimes starts at high idle and sometimes starts at normal idle. Starts great when hot. Mechanic wants to replace fuel distributor, and injectors. I would really like to be sure before I spend the money on a fuel distributor....? Thanks for any thoughts or suggestions...I know this subject gets a lot of attention, but I haven't been able to navigate through the searches to pin point my problem....

Thank you,