You need to perform some voltage drop tests.

1. Place voltmeter across battery & record voltage when cranking starter. Get it when cranking and clicking if possible, especially if the starter is turning slowly. Shouldn't drop below 9.6 volts. If lower make sure the battery is charged up and try again. If still low the starter might be at fault or you could have a bad/corroded connection acting like a big resistor which you will have to find. If the voltage is really high when the no start condition takes place (clickity click) check for loose connections. You could have some worn out brushes on the starter which could give you this or loose ground from the brushes inside the starter. I think the starter is supposed to be sealed. If you remove it, oil could drain from the engine. Might be contaminated with oil??? Not sure. Looking at a breakdown of the starter, the brushes are servicable.

2. Place + lead on solenoid terminal (large one) closest to battery and - lead on large terminal closest to starter. Crank and record voltage (should be really low around .1 volts) This will check the resistance of the terminals on and in the solenoid. Probably do not need to do this since you changed the solenoid but this will eliminate guessing.

3. Place + voltmeter lead to - battery terminal and - voltmeter lead somewhere on bare metal of frame. Crank engine. Voltage should be less than .5 volts. If higher, you have a bad ground connection from the battery to frame.

There are many more checks you can make but this should help narrow things out a bit.

12 Rocket Roadster
03 Bonneville America
69 BSA Firebird Scrambler
73 Yamaha TX 750