why won't my Dodge caliber start or shift out of reverse

If they had doors open for extended periods of time the battery may be dead. Check battery voltage.

The doors were open but the battery was not connected they connected the battery back and the lights work but it won't start or shift

Ok I would still check voltage and battery connections just in case it's dead or connections are loose. Also if your model so equipped the changing of the radio could have set a theft mode. Might want to check your owners manual.

OK I will check all the above and I appreciate the help thanks

If you installed a after market radio,it has and antitheft divice in it,replace it and your car will run,then go find a qualified person to install your radio,with proper control module that has to be installed with your new radio.

what dandy says : )

WOW! Some else has run into this Problem!, LOL!!-Laughing at ME,Not you....I installed an aftermarket Stereo, in my wifes 2008 Caliber, and THE SAME THING, happened..After a few days of pulling my hair out,and many selective words--I re-installed the original radio,re-set the codes, and drove it to the nearest Stereo shop, and had it Professionally installed..Top Shade Tree,, has the Correct Answer!!!

Installing anything in a car now a days can screw up everything from the PCM to the fuse holder.