Well I don't know about your discharged battery being the root of all evil .. I'm guessing she manually activates the overhead lamp? As it should turn off by itself after a few minutes if a door was left ajar .. Skreem module has not been a real issue (repeated issue) that I have seen to really be fully documented with cause / effect issues. Just another theory to go with things.. skreem has "secured" the car so no interaction with the alarm?
The thread on replacing the alarm makes no statements about having to access the skreem, so I would think there is a connector there. Might be able to pull up a replacement alarm module online that would show a pigtail of a sort?