On the side of the starter (under the switch)is the big copper button/contact and its to that the starter switch engages. If that has gotten all burned carboned and/or pitted or worn down too much even a hundred new switches wont fix the problem. Its takes BOTH a good switch andddddddddd a good non pited not worn down non carboned up starter button/contactor.
If things got too hot and arcing under that switch solder may have melted inside the starter resulting in open connections or mechanically stuck/jammed brush holders or burned commutator segments and all other sorts of nasty stuff.
High current draw may have also caused burned carboned resistive connections at battery post and terminals and ground connections and switch to cable connections etc etc. You may have to remove, clean n wire brush, and re attach each n every battery n starter and ground and cable connection.
So you need a good switch,,,,,,,,a starter with no internal damage,,,,,,,,a starter with a not worn out or burned or pitted or carboned button/terminal,,,,,,,,good cables and grounds and connections.
Of course, its possible for a starter to get mechanically stuck/jammed into the flywheel and that causes extreme high current draw which may have damaged the starter or caused burned or carboned connections etc. If you loosen the starter and/or rock the engine over it may free it up...