Hello, the P0560 is a problem with the charging system, alternator, battery or connections in the system. You will need to have the battery charged and then have the charging system testt. The 1626 and 1613 are related to the teft or security system and could very well be the reason it won't run. This system can only be tested with a class 2 scan tool like the dealers use. Here is some basic information on it.
You may experience a start/stall condition with a code P1626 or P1631 set in the PCM. An extended crank condition may cause a code P1626 or P1631 to set when there is no related theft deterrent codes.
To determine if a crank/no start or start/stall condition is being caused by a passlock theft deterrent concern, perform the following steps:
The system can only be tested with a class 2 scan tool like the dealers use. The most common things to go wrong with them are the ignition lock cylinder, and the two small wires inside the steering column that go to the module, tend to break from all of the flexing when the key is turned on and off. But that does not mean that it could not be something else. The big problem with this system is that there is no practical way to work around it or bypass it because part of it is an actual soft ware program that is loaded right into the computer and you would have to write all new software and reprogram the system to even get it to run with out it. You can try to re program the system and see if that will make it work. If not, your stuck until you can find a class 2 scan tool to check it with. A regular code reader won't even access the module for it. Class 2 is the only one that will work. Instructions for re program below. Do it step by step, no short cuts. Good luck.