Troubleshoot Ignition System and Starter

What happens here

With the battery connected, the owner attempts to start the truck by turning the ignition. The starter motor spins but disengages immediately, failing to engage the flywheel. He suspects a problem with the starter solenoid or the starter drive (bendix gear). He pours a small amount of gasoline directly into the carburetor to give the engine a prime, but the truck still fails to start. He then checks the engine compartment for any obvious loose wires or connections that might be preventing consistent power to the ignition system. He finds a black wire leading to nowhere, previously taped, which he cannot immediately identify.

Goal: Identify why the engine isn't starting after battery connection.