You probably have tripped ckt breaker for the starting/charging ckt. Or you could also have a misaligned neutral switch. To make sure it is not the starter do the following troubleshooting. Prep the unit for starting making sure there is cooling water connected through muffs. DO NOT TURN ON THE WATER YET. Remove all plugs and then start it.
Did it crank over? Yes, then you can put back in the plugs. NO, then using a 3/8" or larger screw driver and holding it at its insulate handle, short the two large terminal posts on the starter solenoid. Did it crank over? Yes, you have ignition switch problem (since you said you have a new solenoid installed) either a tripped breaker or a neutral switch is misaligned. No, it means the starter could be bad or battery cables need to be cleaned and re-tightened, or there is a problem with the lower unit preventing the unit from cranking over. Remove the lower unit and try again. The preceding is with all plugs removed.
If from the preceding it cranked over without the plugs, reinstall plugs and turn on cooling water. And then after re-installing the plug it don't want to crank or is too slow to crank over to get it started, do the same troubleshooting again. Short the solenoid with a screw driver, if it cranks over fast enough to start check the solenoid connections making sure it is clean and tight. Visual is not enough you have to disconnect, clean and then reconnect.
If shorting the solenoid doesn't make it crank fast enough still, use jumper cables and jumper the starter straight to the battery terminals both positive and negative. If this makes it crank fast, then you need to check cables from solenoid and battery for clean and tightness. If it still would not crank fast enough, starter is faulty and needs overhaul or replacing.
