1998 Buick ignition failure

My 1998 lasabre wouldn't start while in the garage. Towed to repair shop where it started right after it was taken off the truck. Replaced battery (which was due). Left vehicle at shop where they it started every time they tried over a 3 day period. Took car home and ignition failed while at a shopping center. Took back to shop and again it started. Took to buick dealer and ignition failed while there. They tested lock out and said light was flashig and needed to be replaced. Did so paid $450.00. When they tried to start it after their repair it wouldn't start. Said I needed a new starter. Which component failed or did both fail. They hit on the celenoid and it started right up and I drove it away. However, I know I need a new starter, but did I need the lock out replaced.I don't see where they tested the starter at all before deciding it was the lockout.