2002 mercury 2 stroke will not turn over

by Stephen
(Murfreesboro TN)

This is the first problem I have had with this boat (2002 Triton TR176) since buying in 2008. Don't use it often so had to replace starter battery and trim motor would not raise. Jumped it to the battery and tapped the motor and it worked. Went fishing without a problem other than Bendix not engaging flywheel once. So I clean the starter shaft with brake cleaner and coated with PB Blaster lithium grease. Went to the lake and the starter ran with the key off, so had to disconnect the battery. After letting the boat set for 20 minutes that problem resolved. Next trip out water was 3 footers in every direction and we got out of the wave in a cove, turned the boat off and it would not turn over (as if the battery was dead). No clicking or any noises. While getting towed the navigation light work as did the graph and dash lights. I hit the trim up and lost lights to the dash, but all others were on (trim did not work). Turned the key to on, no problem. Turned the key to run and lost all the dash lights again. After 3-5 minutes the lights came back to bright. Next morning had 12.7 V on battery and on main brass bolts of solenoid with key in run voltage dropped to .3 across brass bolts on solenoid but still had 12.7 at battery. Trim motor does not work from switches, but jumping to battery will go up and down. Don't know what voltage is getting to starter, only saw 2 large gauge wires from ground mounted, one on the bottom and one on the top. No red wire. Had 2 yellow (I think) running from v regulator to under the flywheel.
1) Don't know how to test the 2 small wires off the solenoid
2) Don't know how to test the ignition switch
3) Where to start to find a short to ground

Trim motor is disconnected to rule out it.