To give a quick overview of the function of a starter motor, once the ignition switch is turned the driver is kicked out to engage your engines flywheel. Once the flywheel turns quick enough, it nudges the driver back into the starter motor and the starter motor shuts off.
With that said, the first thing we would advise you to do is to make sure the starter motor is properly installed and lined up correctly within the engine. Check that all bolts are tightened. It should not be loose. Next, and also equally important, is to check and recheck your wiring. Are all cables tightened and in good condition? Chances are, especially with reinstallations, your wires are not where they need go or they are loose. It’s the most common mistake made and easily overlooked.
Check your ignition switch. You want to make sure that the power does not stay on once your ignition switch is released. This continuous power to the starter can cause it not to disengage. To make sure it’s not the solenoid; check the power on the posts behind the solenoid by testing the wire coming from the ignition switch, using a voltmeter. It should indicate zero. If it shows you have power, this may be the reason your solenoid is stay continuously engaged. The reason for this may be a bad switch or the cables may have a short. Please note that switches have been known to work intermittingly.
Lastly, low voltage can also cause this issue. This may be due again to improper wiring, bad connections and a low or bad battery. If after trying these quick-fix solutions you still have the same issue, take your starter off and have it tested as it may be experiencing problems.