Unlock Instructions ignition for Chrysler 300M

Chilton ($25.95) and Haynes ($21.95) both make manuals for the 1999 300M. I would suggest you get one of those for your instructions.

Check that the battery terminals and posts are shiny clean and tight. Have a load test done on the battery as it may be dead.

Hold foot on break , put key in ignition, then with the other hand turn the steering wheel left and then right, right quick and it should start.

needs a new ignition switch. Not too bad for a DIY'er.
Get a book first.

Try key in drivers door, lock, unlock then back to straight. If no luck try passenger as well.

Try to lubricate ignition lock with WD40

it sounds like you have a faulty ignition switch

Manual Programming Procedure (non scan tool)
1. Connect pin 1 of the 16-way data link connector to chassis ground or to pin 4 of the 16-way data link connector.
2. Close all doors, turn ignition key to off.
3. Turn ignition key to Accessory.
4. Turn ignition to off, door locks will cycle once (in programming mode).
5. For each key FOB, press any button 3 times in a row to program code. When programming is complete, the door locks will cycle once.

NOTE:
IF A SECOND KEY FOB REQUIRES PROGRAMMING, IT MUST BE PROGRAMMED WITHIN 1 MINUTE OF PROGRAMMING
THE FIRST FOB PROGRAMMING. PRESS ANY BUTTON ON THE SECOND FOB 3 TIMES TO PROGRAM ITS CODE. WHEN PROGRAMMING IS COMPLETE, THE DOOR LOCKS WILL CYCLE ONCE.

6. The programming mode finishes after the following:
a. Programming of two key FOBS is completed.
b. One minute has passed since programming.
c. Pin 1 of 16-way data link connector is removed from ground connection.
d. Ignition switch is turned on.
e. Any of the doors are opened.

Sounds like the tumblers were messed up. The key shouldn't come out while the ignition is on. If I am right, this has one of those very expensive "Chip" keys? Buying a new key could be more expensive then a lock cylinder. It will probably be cheaper to keep those keys then buy new ones on top of whatever it takes to repair the damage to the lock. You may be better off calling a "Locksmith". Even a new lock cylinder will have to be coded to something. You should be able to find a locksmith that will make a service call.
Let me know how that goes?