The anti-theft system is integrated with the air pump in the rear of the Crossfire. If the anti-theft system is without power (fuse 9) the air pump doesn't work to lock/unlock the doors. The interior lights are also powered by fuse 9; thus if the lights aren't working the pump isn't getting power and the doors will not lock/unlock with the FOB even when the FOB is working correctly. Looking at the interior lights is easy quick way to see if there is power at the air pump. You have several times inspected your FOB and it seems to be okay from what you have told us, so I was looking for another explanation why the car doors were not locking and unlocking. I agree that the likely problem is in the FOB, but it being so easy to check the power to the air pump and anti-theft system it should be checked.

As for the siren, it to is part of the anti-theft system. The batteries leak and over time it will get on the electrical board in the siren which can interfere with the proper operation of the anti-theft system and possible prevent the car from starting. Leaving the siren connected is not a wise thing to do. It is best to open the cowl and replace the siren with a new one or disconnect the electrical connector at the siren so that it is no longer connected to the system. It is also a good time to clear any debris from the four drain lines that are under the cowl as clogged drains will give you addition problems down the road if they do not drain water out of that area.