Hi Guys, I had a similar problem on my 1990 SL. My LEDS stopped working all together after removing my battery. Then all of a sudden the passenger door red LED started to work on its' own! Interestingly the remote locking will still work although the LEDs do not come on, however the alarm will not be armed.

I took the car to a Mercedes dealer who told me I needed new receivers on both doors and boot. Around £350 in parts and labour on top.(around £500). I declined due to the cost.

I then took the car to a non franchised dealer who unplugged the alarm module and then replugged it in. It now works perfectly.
The alarm module is located above the battery in the boot. I suspect that I may have knocked the connector when I removed the battery.

It may be an idea to check this plug.It may save you a lot of money

Regards

Arfan