Welcome to JA.
To disarm the alarm you will need to either lock and unlock the drivers door with the key or put the key in the ignition and start the car. The window should go back up once the battery has been reconnected. Make sure that the rear door is shut good and re-try it. If it still want go back up then the regulator may be broken and jamming. It could have broken when the window went down . These regulators do go out from time to time on these cars. If you have any other questions let me know. Thanks Daniel