You must be trying the wrong code. If you enter the wrong radio code 3 times, the radio goes into "Wait" mode. To fix this, you have to let the car sit with the key on for an amount of time that could be up to several hours, and then try the correct code when the display says "CODE".
Yeah, you probably need to wait. I have a 1986 BMW 528e (not that it's very similar to your C, but the radio issue seems to be about the same). Because I did not have the code, I entered random combinations. The anti-theft light flashed whenever the car was running (not when it was off, as it usually would). My mechanic showed me where the 5-digit code had been scrawled in pencil on a back page of the owner's manual.
If the wrong code is entered into my radio 3 times in a row, you must wait 3 hours before trying again. Do it wrong again, and you must wait 6 hours, then 12 hours, etc. During the wait period, the radio must be left 'on', which necessitates leaving the key in the ignition.