550 Maranello won't start

Hi, Here's my situation, and any advice will be appreciated. For awhile, the small red dot light on the dash has been on. I understand that this indicates the battery for the security system is weak, but I was told that even if this battery fails, while security won't work, the car will operate just fine. Recently, Hurricane Irene passed us by, and we lost power for 5 days. I keep a battery tender on the car, but I do not know if the tender may have not been working properly for some time prior to the storms. In any event, when I ventured into the garage after the hurricane, the battery was low, but not dead. I hooked up a 10 amp charger and restored a full charge. The lights turn on, the battery is definitely charged. However, when I press the button on my key fob, there is no chirp, and the red dot light on the dash is no longer lit. If I put the key in the ignition and turn it to the on position, I get the "Check OK" light, but nothing at all happens if I turn the key to the start position.

Do I need to replace the security battery? If so, is this a job I can do myself? I am mechanically inclined, and have worked on my cars before, but I'm not a mechanic. I had a little water in the garage from the hurricane, but no more than 2" on the floor. No water to the engine compartment. I'm hoping not to have to try to maneuver the car to a flatbed.

Any suggestions are appreciated.