Re: 1994 Mercury 40 hp will not trim or start
Regarding the battery, I'd call a local AutoZone or parts shop in your area. They usually do battery tests for free. Give them a shout and let them know you have a marine battery and what type it is (lead acid, absorbed glass, etc...). They'll be able to tell you if they can test it or not. If they can, it's worth running a simple battery test to ensure the battery is ok.
If the battery is ok, I'd invest in a manual (if you've not already). The SELOC manual I have has diagrams of the electrical system. I'd trace the power source from the battery through the electrical system. Ensure connections are clean and well connected. I'd trace this as much as possible through to the trim motor and starter system. Look for any components common to the starter and the trim motor and see if anything along the way looks suspect.
If you still suspect a starter, I'd look at replacing the cheaper parts first. There's no use buying a new starter if it's only a solenoid. I have a 1991 50 hp and a solenoid runs $23.90 plus shipping. A better first step than replacing a starter.