I have a 2004 Chrysler Concorde LXi 3.5. Couple months ago I was driving pulled over shut car off and went into store..when I can out and tried to start it it just rapid clicks . I let it sit for 20 mins and started right up. Now this week I drove to get gas. Car has been running great. I shut car off and same problem all over again rapid clicks when I try to start except this time it won't start. I let it sit couple days finally it started so I let it warm up. After 20 mins you could see rpm moving up 1 or 2 lines then dropping so got in and started driving. 10 mins after it died while driving now when I start it same thing rapid clicks but now it won't start at all ... I charged the battery and lights go on and static over the radio. So, I went and got a new battery. All lights and radio work great but still clicks and won't start ... any ideas are really could use the help. I only use the car to pick up my kids on my weekends
I think the problem is, one or both of your battery leads are not connected properly. You need to do two things when you installed the new battery. Ensure the leads are completely clean of any type of debris or corrosion. Second, ensure they are tight enough to have a proper and secure connection. I believe the Concorde has side posts on the battery. These can be truly problematic where this can easily happen (even to experienced mechanics).
If the connections appear good, I'd run to the opposite end of these connections and ensure they are attached properly. This would mean that where the positive lead attaches to the starter is in good stead (no corrosion and tight). Then also, follow the negative side back to it's opposite end and make sure it too is clean and securely fastened.
If these also seem good, you may want to take your starter in to have it tested. I don't think it would be the starter, but the starter solenoid which is bad in this case. If it could not make the proper connections internally, it could allow the clicking noise you are talking about. I highly doubt this is the case though, as your car would not just "shut off" while driving if so.
The last thing to check is the alternator. If it is not charging correctly, it would exhibit most (if not all) of these issues.
Ultimately, it could be two or more of these issues occurring simultaneously.