After unlockin the door with the key did you try to start it? Usually putting the key in the ignition and starting it turns off the alarm. The battery in the remote is cheap and easy to replace. Sometimes the chip in the remote pops out and it wont work and you might think the battery was dead then

For the radio, if its not the same one that came with the car, and since they lookup the code by VIN, you can pull the radio and write down the serial number and they should be able to find the code that way. The PO didnt write down the code in any of the manuals?