Hi everyone,
I have a 2002 Mercedes SLK r170 with only 41,000 kilometers (around 25,500 miles) on the odometer. it belonged to my father, and my goal is to fully revive it and get it back on the road in his memory.
I’m dealing with a very frustrating starting issue, and my mechanic is completely stumped. I would really appreciate some insight from the experts here.
The Problem: If the car sits untouched for about a month, it will not start on the first crank at all. In fact, it won’t start until I cycle the ignition key 20 to 40 times (!). Suddenly, on one of those random turns, it will just fire right up out of nowhere without anything else changing.
Once it finally starts, it will continue to start perfectly on the very first try for up to a week. But if I let the car sit again for a few weeks or a month, the exact same cycle repeats—no start until I turn the key dozens of times.
Important details:

• Battery: The battery is constantly hooked up to a charger, so it is definitely fully charged and healthy.
• The K40 Relay: My mechanic suspected the K40 relay module and replaced it with a brand new one, but it did absolutely nothing to fix this specific issue.

Since the K40 is already out of the equation, we are running out of ideas. Could it be a failing crankshaft position sensor (CPS), an issue with the fuel pump losing prime/pressure over time, or perhaps something with the EIS (Electronic Ignition Switch) / immobilizer system?
I would love to hear your thoughts or if anyone has encountered a similar ghost in the machine.
Thank you so much in advance for your help!