I know "0" about this computerized ....@#$%^
I own a 2006 300C, & btw: Love driving this HEMI!! However, when reading the directions to program a new key fob, that little red light was a necessary part of the instruction. It apparently is part of the anti theft (as mentioned before) module & the key reports to it & vice versa.
As already mentioned, change the battery in your fob. I also know that with a new key/fob that is cut using the original and not yet programmed, you can start your car but, it will quit running in a matter of seconds...
My poor husband thought that our truck was very sick....then I pointed out that he had the key that was not programmed...lol!