What needs to be repaired if a starter battery pack was attached to a dead battery in the wrong direction and now dashboard lights still come on but nothing happens when the key is turned?

Could be immobilizer damage, reversing the polarity on modern cars can cause the electronics to fry. Its possible to cross the starter switch wire out to see if engine will start when cranked,if so then its the starter blown but please be aware that you need to know what you are doing to do this as crossing any wires needs to be done by qualified engineer to save electrical or personal damage. Hope this helps