Some topics have lots of good threads already extant... some topics are best found under words not usually used by people...and you did not say that you had searched or tell us the words you used for searching.... and the search has admittedly been suspect lately........ I just did the search and posted the url...
The solinoid is what should take the sliding gear on the starter shaft forward enough to engage the flywheel ring gear.... and some design solinoids would require full movement of the electro magnetic slug in order for the starter to rotate ( because the copper contact point is on the end of the slug )... so all this points to either a messed up engagement mechanism... like broken gear, or malfunctioning solinoid.
Why don't you take the starter/solinoid off the car and to the local parts chain nearest you... they will usually test them free while you watch....