Key replacement and programming?

Okay, replacing the keys won't help because the new keys still need to be programmed into the system. The catch is that car comes in two builds, the convertible and the 4 doors are Chrysler built vehicles while the 2-door coupe is actually a Mitsubishi Eclipse, and they use different security systems. The cylinders will interchange but the keys are different. First be sure which one you have, Coupe or 4 door and convertible. Next take your old cylinder and have a new key cut to fit it and specify which vehicle type it is before they cut the key. Now take it to the dealer and have them program in the replacement keys, because you lost the keys the process is different than just adding extra keys. They should be able to deal with that though.

Okay, the drop top is actually a Chrysler product. The issue you have is strictly involving the ignition cylinder and antitheft being on as a result of the keys not matching the system. Programming the system should solve the issue. The tools locksmiths use can be somewhat hit or miss with vehicle coverage. In this case a dealer level scan tool is needed first as you lost all the keys. Some shops have tools that can do this same process.
This is the factory method -
Using a DRB III Scan Tool
All Sentry Keys included with the vehicle are preprogrammed to work with the Sentry Key Immobilizer System (SKIS) when it is shipped from the factory. The Sentry Key Immobilizer Module (SKIM) can be programmed to recognize up to a total of eight Sentry Keys. When programming a blank Sentry Key transponder, the key must first be cut to match the ignition lock cylinder of the vehicle for which it will be used. The vehicle's four-digit PIN code will be required to complete this task since you will need it to enter the Secured Access Mode in the SKIM. The following steps must be completed using a DRB III scan tool:

1. Insert the blank key into the ignition and turn it to the RUN position.
2. Using a DRB III scan tool, select "Theft Alarm, " "SKIM, " "Miscellaneous, " and then "Program New Key."
3. Enter the four-digit PIN code using the DRB III scan tool. When programming is completed, the SKIM will exit Secured Access Mode and the DRB III scan tool will display the results of your attempt to program the key One of five distinct results may be displayed. All five are listed below:
- "Programming Successful" is displayed if the Sentry Key programming is successful.
- "Learned Key in Ignition" is displayed if the key in the ignition has already been programmed into that vehicle's SKIM.
- "Eight Keys Already Learned (At The Maximum) Programming Not Done" is displayed if eight keys have already been programmed into the SKIM. In this case, if a new key needs to be added due to a lost or defective key, the "Erase All Keys" command (which requires entering the Secured Access Mode) has to be performed. Following the "Erase All Keys" command, all keys that will be used to operate the vehicle MUST be reprogrammed to the SKIM.
- "Programming Not Attempted" is displayed after an "Erase All Keys" function is executed.
- "Programming Key Failed" is displayed if further diagnosis is required.

To learn additional keys, turn the ignition off, remove the learned key, insert the next new blank key, and repeat the steps from the beginning.