Electrical problems

hj everyone ! I have a 2003 Nissan 350z. I hoping someone can tell me if this a electrical problem and how I can fix it if so. My car alarm keeps going off by itself . It will go off all at random times in the middle of the night and during the day. After this last time it went off I went to leave and when I tried to start my car there was no power to the car, when I turned the key over I go no lights or anything. I got a brand new battery just a couple weeks ago, I took it off and took it to advance and had it tested and it's a good battery so I know that's not the problem. When I hook the the little power box up to it to let it trickle charge , I turn the key over and it does get power but will still not start. Is this somethin electrical having to do With the horn going off and no power to the car. Also I have a new starter and had it and the alternator checked and they are fine ! Thanks for any help in advance !!!!!