I have an '83 300SD. When I push down on the brake pedal, I get the brake pad wear light AND the radio goes to STATIC.

I have parts on order to fix the brakes, but What could be causing the radio to have static only when I press the brake pedal down?

The brake pad wear detectors are creating an electrical path to ground through the rotor/hub that does not normally exist. And the anti-static clips in your hubs are probably broken or are no longer installed.

.... which to me means the pads are worn...

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the sooner you start... the sooner you'll get done If it ain't broke, don't fix it.. Its always simpler to tell the truth...
2007 Honda Accord EX
2007 Honda Accord SE V6
96 C220
97 Explorer - Found Another Home
2000 Honda Accord V6 - Found Another Home
85 300D - Found Another Home
84 300D - Found Another Home
80 300TD - Found Another Home
Previous cars:
96 Caravan
87 Camry
84 Cressida
82 Vanagon
80 Fiesta
78 Nova
Ford Cortina
Opel Kadet
68 Kombi
Contessa

I guess I thought that was too obvious to mention!!!

Any idea why my radio does not work in the "OFF" mode?

The radio will only work in the OFF position when it detects an OFF-shore broadcast. Think pirate radio

As for those anti-static clips. they just push in and are pretty easily lost if somebody other than the dealer or YOU do a grease job on the bearings.

They are cheap though

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Current
Monika '74 450 SL
BrownHilda '79 280SL
FoxyCleopatra '99 Chevy Suburban
Scarlett 2014 Jeep Cherokee
Krystal 2004 Volvo S60
Gone
'74 Jeep CJ5
'97 Jeep ZJ Laredo
Rudolf ‘86 300SDL
Bruno '81 300SD
Fritzi '84 BMW
'92 Subaru
'96 Impala SS
'71 Buick GS conv
'67 GTO conv
'63 Corvair conv
'57 Nomad

They also seem to be good at making the transition from a one-piece part to a two-piece part.