It could be a valet switch that is enabled. Which in effect makes the light flash and dodors unlock/lock without setting the alarm itself I believe.
Either try that switch and see what happens, or take it to a shop that does alarms and have them look at it.
'92 300CE - Sold
2004 C240 - C7 Wheels
2015 ML350 - P1, Pano, Ash poplar wood, Sport Dinamica interior, Running Boards Keyless go.