Sounds like your car was finally victim to the notorious "pink thingy" problem. I know it very well, I had to do it to my own 2007 Chrysler 300 Touring
Pretty much what happens, there is this plastic piece that's part of the ignition interlock, it's not really important to know exactly what everything does, you just need to know what has happened. This ignition interlock, which is pink and made from plastic, has most likely broken.
Quite literally it's just a small little hook that connects a small spring to another part on the shifting assembly, and over time, it weakens and eventually breaks. There is a way to get your shifter to move, but it requires some disassembling. Also, do not just take it to a dealership and have them fix it. All they will do is replace the entire shifting assembly, which costs about 300 dollars just for the assembly, and this will happen again.
Go here, http://www.custombilletstore.com/Genuine_Billet_Tech_Pink_Thingy_Replacement_p/1028.htm purchase that part, it is an exact copy of the ignition interlock "pink thingy" but with the added benefit of being constructed out of aluminum, instead of plastic, and see if the techs at a Chrysler dealership will put it in for you, they may or may not.
In the off chance no one can do it for you, here is a very thorough walkthrough of how to do it. http://www.lxforums.com/board/showthread.php/234335-Can-t-shift-out-of-park-into-gear-and-pink-thingy-replacement
And when you buy that part from Billet Technologies, they also send you a PDF file of the entire walkthrough, if you follow it word for word, you will be okay.
From what I've read, Chrysler refuses to issue a recall on this, not surprising since all 2005-2010 Chrysler 300's, Dodge Charger, and every Dodge Magnum made all suffer from this.