I had a similar problem once, and it turned out to be the starter
switch. Inside the key mechanism, there was some corrosion. It caused a voltage drop to the solenoid, which then only partially deployed and caused a voltage drop to the starter
. People often don't think the key switch could cause such a problem, but think about it: That switch is generally located in the cockpit and subject to salt spray. The other components are tucked away safe inside.