Generator will not crank

We have a 2006 38 DA that our marina left the batteries attached over the winter (Boston area). In the spring the port side was dead but we emergency started it. The port side still would die quickly and when I tried the gen it wouldn't turn over. Bought new batteries but then found two fuses (control and one other) and the switch was thrown. Now it clicks but no crank. After going through 3 cycles it shows OC (Over Crank). I have heard it is the control board $$ and I have heard it could be the solenoid. Can anyone tell me how to test?

The following is from the service manual. It's a bit broken because I copied it from the table in the service manual.
Good luck and welcome to CSR!

Generator does not crank:
Weak or dead battery Recharge or replace battery. Generator O/M
Battery connections Check for reversed or poor battery connections. —
Open circuit in engine/controller connections Check for loose connections.
Check the wire harness continuity. Section 7
Blown fuse F2, controller Replace fuse; if fuse blows again, check circuit and components. Section 5.12 Section 7
Blown fuse F2, relay interface board (RIB), Replace fuse. Section 5.12
board If fuse blows again, disconnect the board leads one at a time to identify the cause of the blown fuse:
Lead 70A
Leads FP and FN at the rotor
Repair or replace the component causing the blown fuse. Section 7
If fuse continues to blow and the previous step did not identify the cause, check the continuity of leads FP and
FN and the leads from the P14 connector. Replace any bad leads. Use a pin pusher, part #241918 (large) or
241919 (small) to remove leads from the connector, if necessary. If replacing the leads does not solve the
problem, replace the RIB. Section 7 Section 4.6
Crank relay on relay interface board (RIB) Check connections to the RIB. Check for 12VDC to the RIB on lead 71N.
Section 4.6 Section 7
Check for a good ground connection (lead N). Section 7
Check crank relay K2 operation (LED3). Replace the
RIB if relay does not operate. Section 4.6
Generator set master switch Check connections to the master switch on the ADC 2100. Section 4.3 Section 5.13
Test function of switch. Section 5.13
Poor ground (--) connection Clean and retighten. —
Starter Check starter connections. Section 7
Rebuild or replace starter. Engine S/M
Controller Check controller connections and operation. Check for power to the controller. Move generator set master
switch to OFF/RESET and then to RUN. Section 4 Section 7
Blown F3 fuse Verify line circuit. Section 7
Blown F6 fuse Check voltage regulator wiring. Section 7
Blown F7 fuse Check wiring for open grounds or loose connections.
Also, check for pushed out pins. Section 7

Thank you Jim,,,, I will try this on Friday. The closet Kohler dealer will not get to it for weeks.

Mine did this and I found out it was hydro-locked... I hope this is not the case with you... I originally thought it was a bad starter, but it was not...