AD, my 1995 E320 wagon just had the same issue (7/24), and I placed my hand on the rear of the engine-bay fuse box, and I could FEEL some relay buzzing, and there was NO BLINKING Alarm LED.

Based-upon all the late model W124's having this problem, I wonder if this is some impending failure mode for either the ATA, NSS module, or their respective relays, or OVP ?

In a different thread, I was successful by disconnecting the OVP relay for 5-seconds; locking & unlocking the door a couple of times; and then when I saw the courtesy light on, she started up fine.

Battery was replaced in 2005, and she sat on battery charger for 2-days, and she has a new OVP relay (2-days ago); a new NSS (2-months ago); and all fuses were changed out in October 2007.

Hmm . . .

:-) neil