Somebody has tampered with your antennas; for what purpose I do not know.
First, there should not be that connector protruding through the sheet metal on the roof. It is no part of any original Mercedes installation. I have no idea what it was for.
Second, your "shark fin"antenna looks as if it has been taken off and re-glued. That antenna contains your GPS antenna and one of two cell phone antennas (the second cell phone antenna, at least in North American cars, is in the rear bumper).
Your AM and FM radio antennas, as well as the antenna for the door locks are in the glass of your rear window. They connect to several low-powered linear amplifiers located between the sheet metal of the roof and the headliner, just in front of the rear window frame. Loss of AM and FM radio is likely the result of failure of these amplifiers.
If your rear window has metallic tint applied over the glass, this will also cut down reception. Only ceramic-based tint should be used.
Your smart key operates on both radio frequency (with the signal being received at the rear window) and Infrared (with the signal being received at the black square lens in the door handle). Apparently the key is functioning with infrared, so its batteries are likely good. However, the potential sources of problems are a bad circuit in the key, and a bad linear amplifier (next to the radio amplifiers; all go on the same mounting bar).
Although your car is quite different from the later model W220s, the general operating principles of the antenna system are the same; specifics may differ. See http://www.benzworld.org/forums/w220-s-class/1834026-w220-antenna-system-key-fob.html
Also, for the key, see http://www.benzworld.org/forums/w220-s-class/1646105-battery-died-now-key-wont-unlock.html - and especially, try the steps at post 24.
First, there should not be that connector protruding through the sheet metal on the roof. It is no part of any original Mercedes installation. I have no idea what it was for.
Second, your "shark fin"antenna looks as if it has been taken off and re-glued. That antenna contains your GPS antenna and one of two cell phone antennas (the second cell phone antenna, at least in North American cars, is in the rear bumper).
Your AM and FM radio antennas, as well as the antenna for the door locks are in the glass of your rear window. They connect to several low-powered linear amplifiers located between the sheet metal of the roof and the headliner, just in front of the rear window frame. Loss of AM and FM radio is likely the result of failure of these amplifiers.
If your rear window has metallic tint applied over the glass, this will also cut down reception. Only ceramic-based tint should be used.
Your smart key operates on both radio frequency (with the signal being received at the rear window) and Infrared (with the signal being received at the black square lens in the door handle). Apparently the key is functioning with infrared, so its batteries are likely good. However, the potential sources of problems are a bad circuit in the key, and a bad linear amplifier (next to the radio amplifiers; all go on the same mounting bar).
Although your car is quite different from the later model W220s, the general operating principles of the antenna system are the same; specifics may differ. See http://www.benzworld.org/forums/w220-s-class/1834026-w220-antenna-system-key-fob.html
Also, for the key, see http://www.benzworld.org/forums/w220-s-class/1646105-battery-died-now-key-wont-unlock.html - and especially, try the steps at post 24.