Help - Starter Stays Engaged (1990 GEO)

My 1990 Geo Prism (GSI?) now has the starter engaged whenever the battery is connected (even with Ignition Key out!). Is this most likely a need to replace the starter, or should I be thinking of something else (like the wiring from battery to starter) as more likely? Over previous weeks, the turn of the key would sometimes get a "click" only, and then a start after another try or two. Battery itself is pretty new.

(Note: when this first happened, the starter kept going for at least a full minute or 2 before I pulled the battery terminal. Have I possibly caused problems (flywheel) beyond just a starter/wire replacement anyway?)