can't disable car alarm

I have a 91 BMW 3-series with an alarm, keyless entry, etc. I do not think that the alarm is stock but can't say for sure. I do not know the brand of the alarm.

A few days ago the battery in my remote entry keychain died. I needed to get in the car anyways so I used my key to unlock the door. The normal alarm (multi-sound cycle) went off when I closed the door but then when I locked the door with the key the alarm disengaged. I then unlocked the car and was able to start it with no problems.

The next day I needed to put something into the car. I unlocked it just fine, the alarm was still disengaged, but the thing I was putting into the car banged against the under-carriage of the car by the driver-side door causing some non-normal alarm (a repeating single tone) to go off. This incident also disabled the ignition and locking/unlocking the car using the key did not disengage it.

I got a new battery for my remote entry but no combination of buttons (it has several) has any effect. I also disconnected the car battery to no effect.

There are two buttons on the dash (one looks like it has a sun-beam-like pattern on it, the other is plain) that seem to be related to the alarm (in the past pushing the buttons would cause the alarm to chirp). I have tried various combinations of button pushes while putting the key into the ignition to no effect.

Can anybody give me some idea of how to reset my alarm?