The Key can still start the car if the transmitter goes bad. Mine did the same thing. I had to take my VIN and Registration to the dealer so they could order new keys. They cost about $100 each and according to the dealer required the keys to be programmed using the Chrysler Diagnostic tool. ( Although I never tried the procedure above )
Some Parts stores have a Key Fob tester that will test if a signal is coming out of the transmitter. Most Autozone stores have them. I would try that first.
I am now very careful with my keys now. Mine died after my 2 year old dropped them.