My daughter pulled the keys out of the ignition while in the lock position. We replaced the cylinder so it doesn't keep turning but won't start. could she have broken starter switch at same time?

When you installed the new lock and you said a piece of metal was broke what does the piece look like and where is it from exactly? You might have broken off the tab that actuates ignition? I would get the switch issue resolved before doing any work on the starter.

I didn't see the piece that broke off, my husband didnt see it either just the place on the key cylinder where it appeares a little piece came off, it was at the edge furthest from where the key is inserted. One of the times I was trying to start it after this happened it felt like something caught where it should, the engine just started to turn over but then it felt like something slipped, the key again turned past where it should, and it died, so maybe what you mentioned? Is that part of the ignition switch? I was thinking if it was still starting then the starter itselfn wouldn't be a likely issue unless I am just not clear on what it does. Thanks

Check to make certain that the lock cylinder is inserted all the way into steering column.