Starting problems 2004 Yanmar 3gm30f

[Tortuga331]

Hello,
The other day I went sailing. It started fine. I motored for 20 min to work the engine before sailing. After 2 hours of sailing, engine would not start.
I got towed in and plugged into shore power, after 2 minutes , it started right up. I figured it had to be batteries, so I bought 3 new batteries. I noticed when I started it up,after new batteries were installed, Red light saying "Charging" lit up and did not go off like usual after starting. I don't know if I have a bad charging system , bad alternator or possibly starter? How would I go about checking these things? BTW I called 3 mechanics , they are booked solid.
I would appreciate some comments, You all helped me so much in the past by Diagnosing my LIFT PUMP that went last year.

thanks all,
Bill
Tortuga