No crank. slow crank and stuck starter solenoid problems have the same root causes – low battery voltage and poor connections
A voltmeter placed across the battery terminals should show a minimum of 9.5-10 volts when the ignition switch is turned to the Start position and the starter engages or tries to engage. Less than this will result in a clicking solenoid, or slow cranking (if it cranks at all) or a starter solenoid that sticks and welds the contacts together.
If the starter solenoid welds the contacts, then the starter will attempt to run anytime there is power in the battery. The cables and solenoid will get very hot, and may even start smoking. The temporary fix for a welded starter solenoid is to disconnect the battery and smack the back of the solenoid housing a sharp blow with a hammer. This may cause the contacts to unstick and work normally for a while.
Some suggestions for all type of cars:
The battery posts and inside of the battery post terminals should be scraped clean with a knife or battery post cleaner tool. This little trick will fix a surprising number of no start problems.
The clamp on with 2 bolts battery terminal ends are a know problem causer. Any place you see green on a copper wire is corrosion. Corrosion gets in the clamped joint and works its way up the wire under the insulation. Corroded connections do not conduct electricity well. Avoid them like the plague...