Car will start but as soon as the key is released back to the "On" position, it dies. Happens mostly when the car is "cold" and less after the car has been run.
Seems like an ignition switch problem but I'm not sure. If so, how big of an issue is it to replace the switch?

Before you get involved changing the ignition switch which by the way is mounted on the steering column under the dash, when you release the key to go back to the run position do all the dash warning lights go out too or just the engine quits?

I will find out. It is my daughter's car. It was parked in the garage last night (not typically). I tried it this morning and it started and stayed running.