I would guess that the erratic chime and start have something to do with the EWS antenna not seeing the key properly. And I'm guessing you only have the 1 key ?? Has someone tried to install a remote start ?

__________________
1988 325is (purchased new) sold
2004 X5 3.0 2005 X3 2.5
2008 X5 3.0 (new to me)