Is it 6-volt or 12-volt? 9 times out of 10 when the starter just clicks or does nothing when ignition switch is engaged points to a bad battery. How old is it? When you took your starter to your local shop you also should have taken your battery to get tested as well. The battery must sustain a charge under load, and he has the right test equipment to analyze it. Next, I would not loosen the starter bolts and try to crank the engine over. That is a good way to damage something like breaking the Bendix drive. Just replacing parts ("...put a new solenoid in since I had it just sitting around...") without knowing if good or bad is not a logical root cause problem solving method. Next step is to verify the wiring is correct.
Tim Daley(MI)