Didn't drive my 2006 GT for a couple of months...tried to start it and was dead, but when jumping it, the key code security is activating and the alarm just starts going off

Do I have a dead battery or bigger issue?

 

Probably just the battery. The OE batteries don't hold up (do a search and you'll see all kinds of dead battery threads) too well. Even with a jump, the alternator will struggle to charge the battery and may result in a low voltage condition that'll cause all KIND of gremlins. Put a new battery in and see how she responds.