1004 RX330 wont crank or start

[bannis4]

I have a 2004 RX330 that was running fine.  The other day the battery was dead and I jumped the car and it started right up.  I guess the battery didn't charge all the way because I tried to start it back up again and it wouldn't.  I tried to jump it again....this time the alarm/horn sounded constantly.  I disconnected the cables and started over.  I put the key in the ignition, in the on position.  Left the door open, hooked up the cables.  The alarm sounded this time but not a constant blast of the horn.  After leaving the cables hooked up for a while it still wouldn't start so I went and got a fresh battery.  The car will respond to the keyfob, doors lock and unlock.  When I put the key in the ignition and turn it the dash cluster lights up but the car wont crank.  I cant get the radio to come on, the windows wont roll down.  All I get is the dome light and instrument cluster.  I went through and checked fuses and everything looks fine. 

Curious if this could be something with the security system or something else.